1 Introduction

Up to 70% of the primary energy used by cities is consumed by buildings [1]. According to a report series of heating ventilation, and air-conditioning (HVAC) factsheet [2], HVAC systems in general, utilize over 70% of the base energy used in buildings, with chillers consuming more than 40% of the energy in the production of chilled water for air-conditioning [3]. Salamone et al. [4], predicted that this rate of increase would continue since high energy consumption in commercial office buildings is becoming more visible as economies develop and people's quality of life improves. It is becoming more common to construct commercial buildings with wide or completely glazed facades, transforming them into "glass boxes" that expose most or all of their frontages to high daytime temperatures and radiation [5], resulting in thermal discomfort inside indoor spaces. To improve the effectiveness of such exposure, intricate HVAC systems which come with their own set of challenges including high energy consumption and increased carbon dioxide (CO2) emissions into the environment are used in commercial buildings. According to Chua et al. [6], the energy used by an HVAC system in tropical climates may be more than 50% of the building's overall energy use. In Ghana for instance, data and market studies carried out show that between 60 and 80% of the energy consumed in offices for active work is consumed by air conditioners [7]. As a result, efficient HVAC plant energy management is becoming increasingly necessary to preserve energy and minimize the impact on the environment [8]. Conversely, chiller plant management is difficult and time-consuming.

A chiller system with a fan coil, one of the main HVAC systems, is frequently used in commercial buildings for comfort cooling because of its easy-to-use design regulation. By supplying the low-temperature chilled water to the fan coil installed in the room, the excess humidity and heat could be removed. Systems for chilled water are usually designed to deliver a full cooling load with a corresponding chilled water temperature value. However, plant operators normally leave the chilled water temperature set at this level, which is wasteful for the majority of applications, including air-conditioning, because the load is often below its maximum [9]. Similarly, the water-cooled chiller at the Takoradi Thermal Power Plant Office building in Ghana is run by invariably setting the chilled water temperature setpoint to a default value of 12.5 °C to ensure adequate capacity for the majority of the peak loads. Notwithstanding, when there are exceptionally high outside air temperatures, the chiller is unable to condition the spaces, therefore, the setting is adjusted to 10 °C. In moderate weather, however, cooling capacity may exceed demand, resulting in energy waste [10]. Therefore, the setting is readjusted to 14 °C. Regardless, even with a partial load, the chiller system operates at full capacity when such control settings are used. It is crucial to thoroughly study the effect of the chilled water temperature setpoint on the energy performance of the chiller system and the indoor thermal comfort conditions.

Engineering experiments test hypotheses and examine novel components, procedures, or materials for a specific application, providing the foundation for scientific knowledge. Therefore, if numerical and analytical models are not based on valid experimental evidence, it becomes meaningless [11]. Using a thermodynamic model of an air-cooled screw chiller created in TRNSYS, Yu and Chan [12] demonstrated how to adjust the setpoint of the condensing temperature for enhancing the coefficient of performance (COP) of air-cooled chillers under various operating situations. It was discovered that the condensing temperature setpoint affects both the chiller COP and the necessary airflow for heat rejection under any given operating condition. Strategies for increasing the energy efficiency of air-conditioning systems in commercial buildings were reported in [13,14,15,16]. As part of the strategies, heat pump and water-cooled air-conditioning (AC) system integration were implemented and heat rejection in the condenser and cooling tower enhancement were used to lower the energy consumption of water-cooled AC systems. Likewise, the efficiency of one of the components of a chiller plant was improved by Zhuang et al. [15]. Chang [16], developed a model of a chiller using a simulation tool. The optimal temperature setpoint of condensing water for chillers was identified and managed to avoid fluctuations in chiller efficiency under various operating situations. It was discovered that when the chilled water system operates at optimal chilled water pump head, chilled water supply temperature, and other setpoints resulted in significant energy savings.

The aforementioned studies have demonstrated that the energy efficiency of the chiller system can be increased using several novel control strategies. However, the thermal comfort gained as a result of the energy savings was not evaluated. Meanwhile, thermal comfort is one of the key factors in occupant satisfaction with the built environment [17]. Yun [18] investigated how thermal comfort and energy use are affected by perceived control using dynamic building energy models. The simulation showed that altering the occupants' perception of their level of control over the thermal environment could lower the amount of energy needed to cool a building without reducing the thermal comfort of those inside. To examine thermal comfort and energy savings in public buildings, Ferreira et al. [19] applied a model-based predictive control method using the branch and bound method to analyse the HVAC system’s performance. The results showed a significant energy saving. In other studies, the effect of thermal comfort on building energy consumption has been predicted by several researchers using the PMV model. By taking into account each occupant's metabolic rate, Hong et al. [20] evaluated the energy and thermal comfort in a residential building utilising PMV control. Their research demonstrated that PMV control can increase thermal comfort and decrease the load. Similarly, office buildings with natural ventilation were explored and certain thermal comfort methods were examined by Moujalled et al. [21]. They concluded that operating costs and cooling energy are reduced when occupants accept greater indoor temperatures. For indoor thermal comfort and energy savings at high outdoor temperatures, Amoabeng et al. [22] varied the indoor setpoint temperature of a split-unit air conditioner and discovered that 21 °C and 25 °C are the least and best setpoint temperatures using Energy Plus and PMV for the modelling and simulation. In addition, efforts were made by Karami et al. [23] to reduce energy usage in school buildings while also guaranteeing adequate indoor environmental conditions. Also, using occupant feedback on thermal comfort, Dutta et al. [24] controlled the setpoint temperatures of distinct zones. The findings showed that even if the occupants are used to cooler indoor temperatures, an increase in setpoint temperatures had no adverse effects on their thermal comfort. Mancini et al. [25] showed in their study that, by altering the airflow rates handled by the HVAC system, the energy usage and indoor air quality (IAQ) of a building can be assessed.

During the literature review, there is no study on the optimum performance of the chiller system in terms of both energy saving and thermal comfort by increasing the chilled water temperature setpoint. Nevertheless, chillers can have their chilled water temperature raised without having a negative impact on the chillers [9]. Therefore, raising the chilled water temperature is applied to ensure energy efficiency; however, the precise power usage and indoor thermal conditions are often not known.

The study aims to predict the chilled water temperature setpoint that optimises the chiller system for both thermal comfort and energy saving and also presents a prediction model for the power consumption, air temperature, and relative humidity for each chilled water temperature setpoint reset. The results of this study have significant implications for energy professionals and building managers, especially in hot, humid areas [26]. The uniqueness of this work is in the mixed methodology (experimental and numerical modelling (CFD, and PMV-PPD)) employed to fill the research gap in a different climatic region (Ghana). The study's originality is also enhanced by the use of data from a real-world chiller system.

2 Materials and Methods

The following data-gathering procedures were employed to collect quantitative information about the real conditions: (1) a physical measurement of various characteristics that affect thermal comfort, (2) PMV-PPD and CFD modelling of the occupied space at the various chilled water temperature setpoints (CWTS) and prediction model for the power consumption, air temperature, and relative humidity for each chilled water temperature setpoint reset.

Experiments on a water-cooled chiller-fan coil system installed at the Takoradi Thermal Power Plant Office building situated at Takoradi, Ghana (\(4.9716^\circ \,\mathrm{ N}, 1.6586^\circ \,\mathrm{ W}\)), were conducted. The chiller system which serves the drivers’ office consists of a water-cooled chiller that serves nine (9) fan coil units, a pump serving nine (9) fan coil units, and each fan coil unit serving two or three dedicated rooms in the office complex. The chiller system is coupled to a seawater reservoir for heat exchange. It comprises a water-cooled chiller with a cooling capacity of 240 kW, a 25-kW fan coil unit (direct-drive, forward-curved blower which produces 1.89 m3/s supply air), a condenser water pump of 16 kW capacity and a 9.2-kW capacity chilled water centrifugal pump. The schematic diagram and images of the chiller system are shown in Figs. 1 and 2. The experiment was limited to one room (the drivers’ office—5100 mm × 3560 mm × 2743.2 mm) due to availability.

Fig. 1
figure 1

Schematic diagram of the Chiller system used in the test site

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Fig. 2
figure 2

The chiller system (a) and fan coil unit (b) installation at the test site

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The plan of the experimental room (drivers’ office) and the internal view of the experimental room are shown in Figs. 3 and 4, respectively. The drivers’ office has a table, chairs, and a cabinet with an occupancy of six (6) people at any point in time. The drivers’ office has two diffusers of dimension 650 mm × 440 mm positioned at 1300 mm away from each opposite wall. The ceiling material was constructed of gypsum tiles with the roofing material being concrete, and the room was fitted with a galvanised moulded door, brick wall, and a glass window.

Fig. 3
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The test site’s floor plan

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Fig. 4
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The inside view of the test room (drivers’ office)

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A data collection experiment was carried out to record the power consumed and indoor parameters at each chilled water temperature setpoint. The experiment was conducted during an occupancy period, from 7:00 am to 4:20 pm, Monday to Friday for three (3) consecutive days, for each chilled water temperature setpoint (10 °C, 12.5 °C, and 14 °C). Measurement of indoor environment parameters (relative humidity, air temperature, and face velocity) was taken from a height of 1.1 m above the ground level as recommended by ASHRAE standard 55-2010 [27] and 1.5 m. The power consumption by the chiller system was recorded with a Fluke 345 power quality clamp meter within one (1) minute intervals continuously throughout the experimental period. The instruments used to collect the data included an anemometer, an energy meter, temperature, and humidity sensors. Before each experiment, all of the equipment were calibrated to guarantee that the readings were reliable and accurate. Presented in Table 1 is the list of major instruments used to undertake the experimental work. The sensor types, measurement types, instrument ranges, and accuracies have also been presented.

Table 1 List of Instruments and corresponding specifications
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The clothing values, metabolism rates, and different air velocities derived from the literature were integrated with the mean indoor ambient parameters such as relative humidity and temperature values [28] to compute the predicted mean vote (PMV) as well as the predicted percentage of dissatisfied occupants (PPD), by the use of the software application, CBE thermal comfort tool [29]. The air velocity employed was 0.1 to 0.4 m/s, as suggested in the work by Szokolay [28].

3 Numerical Modelling

The predicted mean vote (PMV) and predicted percentage dissatisfied (PPD) models shown under the ASHRAE thermal comfort criteria were employed in this study. The PMV is a predictor of the average value of a significant number of people’s votes on a thermal comfort scale that depends on the equilibrium of the heat balance within the body. Thermal comfort is influenced by many elements [30]. These include environmental elements such as air temperature and personal factors such as metabolic rate [31]. The PMV values can be employed to determine whether or not a specific thermal environment meets comfort standards and to set requirements for various levels of acceptance [32]. The predicted percentage dissatisfied model which forecasts the average value of thermal votes from a wide sample of persons who have been exposed to similar environmental conditions was calculated. The total number of individuals who are probable to experience uncomfortably cold or warm was also calculated using individual votes. The means of relative humidity and air temperature at the various CWTS were used with air velocity, metabolic rate, and clothing insulation in the PPD modelling. Using the PPD model index, the proportion of thermally dissatisfied people who experience warm or cold was predicted quantitatively. References were made to the ISO 7730-2005 [33] standard which defines thermally dissatisfied persons as those who, on the seven-point scale of thermal sensitivity, vote hot, warm, cool, or cold as presented in Table 2. Figure 5 shows the relationship between PPD and PMV. The PPD which is generated using the PMV, is obtained from the combined distribution of individual thermal sensation votes. It decreases whenever PMV approaches zero [34]. According to ASHRAE 55-2017, to provide thermal comfort, all occupied areas of space should be kept below 10% PPD and PMV should be within the range of − 0.5 to + 0.5. The symmetrical curve has a minimum value at PPD of 5% at − 0.05 PMV. It is evident that PPD never reaches zero. As a result of the near impossibility of satisfying every member of a large group in the same indoor climate. The PMV model is computed using Eqs. (1)–(4) [33], and the PPD is computed using Eq. (5) [33].

$$ \begin{aligned} {\text{PMV}} & = \left[ {0.303 \cdot \exp \left( { - 0.36 \cdot M} \right) + 0.028} \right] \\ & \quad \cdot \left\{ {\begin{array}{*{20}l} {\left( {M - W} \right) - 0.303 \cdot 10^{ - 3} \cdot \left[ {5733 - 6.99 \cdot \left( {M - W} \right) - p_{\text{a}} } \right] - 0.42 \cdot \left[ {\left( {M - W} \right) - 58.15} \right]} \hfill \\ { - 1.7 \cdot 10^{ - 5} \cdot M \cdot \left( {5867 - p_{\text{a}} } \right) - 0.0014 \cdot M \cdot \left( {32 - t} \right)} \hfill \\ { - 3.96 \cdot 10^{ - 8} \cdot f_{{\text{cl}}} \cdot \left[ {\left( {t_{{\text{cl}}} + 273} \right)^4 - \left( {\overline{{t_{\text{r}} }} + 273} \right)^4 } \right] - f_{{\text{cl}}} \cdot h_{\text{c}} \cdot \left( {t_{{\text{cl}}} - t_{\text{a}} } \right)} \hfill \\ \end{array} } \right\} \\ \end{aligned} $$
(1)
$$ \begin{aligned} t_{{\text{cl}}} & = 35.7 - 0.028 \cdot \left( {M - W} \right) - I_{{\text{Cl}}} \\ & \quad \cdot \left\{ {3.96 \cdot 10^{ - 8} \cdot f_{{\text{cl}}} \cdot \left[ {\left( {t_{{\text{cl}}} + 273} \right)^4 - \left( {\overline{{t_{\text{r}} }} + 273} \right)^4 } \right] + f_{{\text{cl}}} \cdot h_{\text{c}} \cdot \left( {t_{{\text{cl}}} - t_{\text{a}} } \right)} \right\} \\ \end{aligned} $$
(2)
$$ h_{\text{c}} = \left\{ {\begin{array}{*{20}l} {2.83 \cdot \left| {t_{{\text{cl}}} - t_{\text{a}} } \right|^{0.25} \quad {\text{for}}\; 2.83 \cdot \left| {t_{{\text{cl}}} - t_{\text{a}} } \right|^{0.25} > 12.1 \cdot \sqrt {{v_{{\text{ar}}} }} } \hfill \\ {12.1\sqrt {{v_{{\text{ar}}} }} \quad \quad \quad \;\;{\text{for}} \;2.83 \cdot \left| {t_{{\text{cl}}} - t_{\text{a}} } \right|^{0.25} < 12.1\sqrt {{v_{{\text{ar}}} }} } \hfill \\ \end{array} } \right\} $$
(3)
$$ f_{{\text{cl}}} = \left\{ {\begin{array}{*{20}l} {1.00 + 1.290l_{{\text{cl}}} \quad {\text{for}}\; l_{{\text{cl}}} \le 0.078 \;{\text{m}}^2 \;{\text{K}}/{\text{W}}} \hfill \\ {1.00 + 0.645l_{{\text{cl}}} \quad {\text{for}}\; l_{{\text{cl}}} \le 0.078\; {\text{m}}^2 \;{\text{K}}/{\text{W}}} \hfill \\ \end{array} } \right\} $$
(4)
Table 2 The seven-point scale of thermal sensations [33]
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Fig. 5
figure 5

The relationship between PPD and PMV [33]

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1 metabolic unit = 1 met = 58.2 W/m2, 1 clothing unit = 1 clo = 0.155 m2 °C/W [33]

$$ {\text{PPD}} = 100 - 95 \cdot \exp \left( { - 0.03353 \cdot {\text{PMV}}^4 - 0.2719 \cdot {\text{PMV}}^2 } \right) $$
(5)

The implemented boundary conditions in the ASHRAE-55 thermal comfort modelling approach are presented in Tables 3 and 4.

Table 3 Statistical summary of indoor parameters
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Table 4 Subjective reactions to air movement [28]
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4 Modelling Using Computational Fluid Dynamics (CFD)

The CFD model was developed to study the indoor environment conditions of the office at different chilled water temperature setpoints (10 °C, 12.5 °C, and 14 °C). The CFD analysis was performed using Fluent which is available in the ANSYS Workbench version 2020 R1 software package. The ANSYS Workbench software package was selected because it has been used in a similar study [35]. The following assumptions were made:

  1. 1.

    The flow is assumed to be transient.

  2. 2.

    The internal and external sources of heat (solar radiation and room occupants including lights and equipment).

  3. 3.

    No-slip on the walls.

  4. 4.

    The surface wall temperatures of the room were assumed to be the same as the room air temperatures.

In this study, the numerical model used was based on solving the three governing laws which include; the Navier–Stokes equation, the continuity equation, and the energy equation [36]. The Navier–Stokes, continuity, and energy equations were used to characterise the momentum, mass, and energy conservation of the heat transfer process (air), respectively. The turbulent model employed in this work was the turbulent kinetic energy, k, and the rate at which it is dissipated, \(\varepsilon \). The transport equations below are used to account for these models [37]:

$$\frac{\partial }{\partial t}\left(\rho k\right)+\frac{\partial }{\partial {x}_{i}}\left(\rho k{u}_{i}\right)=\frac{\partial }{\partial {x}_{j}}\left[\left(\mu +\frac{{\mu }_{t}}{{\sigma }_{k}}\right)\frac{\partial k}{\partial {x}_{j}}\right]{G}_{k}+{G}_{b}-\rho \varepsilon -{Y}_{M}+{S}_{k}$$
(6)
$$\frac{\partial }{\partial t}\left(\rho \varepsilon \right)+\frac{\partial }{\partial {x}_{i}}\left(\rho \varepsilon {u}_{i}\right)=\frac{\partial }{\partial {x}_{j}}\left[\left(\mu +\frac{{\mu }_{t}}{{\sigma }_{\varepsilon }}\right)\frac{\partial \varepsilon }{\partial {x}_{j}}\right]{C}_{1\varepsilon }\frac{\varepsilon }{k}\left({G}_{k}+{{C}_{3\varepsilon }G}_{b}\right)-{C}_{2\varepsilon }\rho \frac{{\varepsilon }^{2}}{k}+{S}_{\varepsilon }$$
(7)

Equation 8 gives the convective heat and mass transfer physics for \(k-\varepsilon \)

$$\begin{aligned}&\frac{\partial }{\partial t}\left(\rho E\right)+\frac{\partial }{\partial {x}_{i}}\left[{u}_{i}\left(\rho E+p\right)\right]\\ & \quad =\frac{\partial }{\partial {x}_{i}}\left[\left(k+\frac{{c}_{p}{\mu }_{t}}{P{r}_{t}}\right)\frac{\partial T}{\partial {x}_{i}}+{u}_{i}\left({\tau }_{ij}\right)eff\right]{S}_{h}\end{aligned}$$
(8)

The geometric model of the room (drivers’ office) in three dimensions including the inlet diffusers and the outlet grille and the occupants in the room was created to replicate the actual room at the office building. The 3D geometric model was created in the Space claim environment which is part of the ANSYS Workbench software suite version 2021 R1. The geometric models developed included the human model of the drivers, the office table, the chairs, the outlet, and the inlet grilles. The model was developed to capture the environmental conditions of the office during the flow simulation. The model of the office was created using the actual physical dimensions of the drivers’ office (length of 5100 mm, width of 3560 mm, and height of 2743.2 mm). Six manikins were created with the assumption of maximum occupancy in the test room. The model (test room) together with its components was meshed. The mesh statistics include 8,059,123 elements and 2,417,271 nodes. The selected mesh size was 0.04. Presented in Fig. 6a–c are the images of the geometric and meshed models, respectively.

Fig. 6
figure 6

Geometric (a) and meshed (b) models of the office with its occupants

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The material properties (physical and thermo fluid properties) of the fluid and geometric model components of the office including its occupants are summarised in Tables 5 and 6.

Table 5 Fluid material properties
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Table 6 Solid material properties
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The climatic conditions normally existing in Takoradi, Ghana, were assigned using the solar model which is an inbuilt feature in ANSYS Fluent. The geographical position system coordinates (latitude and longitude), time of day, month, and building orientation (East–West) were inputted into the solar load model resident in the Fluent system. The solar load (radiation) model which characterises the physical system was enabled. The model has been thoroughly used in the studies of [38,39,40]. It uses a solar calculator to compute the solar flux and its dependent on the time (time, time zone, and date) and the geographical location (latitude and longitude). This solar calculator model accounts for the motion of the sun due to daytime as the sun traverses the sky. The assumed days for the solar load modelling were the same as the days used for the experimental setup (June 30 to July 10, 2020). The solar radiation was modelled by considering solar radiation from the window as well as the contribution of solar radiation to indirect thermal diffusion from the walls. This allows for the cooling phenomenon to be approximated. The boundary conditions were assigned using information from Tables 7, 8, and 9. Figure 7 shows the locations of the various boundaries of the test room. The average measured room air temperature at the onset of the experiment was used as the initial boundary conditions in the CFD modelling.

Table 7 Boundary conditions employed in the simulations
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Table 8 Boundary conditions employed in the simulations
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Table 9 Boundary conditions
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Fig. 7
figure 7

Boundary conditions of office

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Model validation was conducted using the mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), relative difference (RD), and the percent bias (PBIAS) models to check the goodness of fit and for comparison. Both experimental and predicted (CFD simulations) results were used to compute for goodness of fit. The aforementioned validation model has been extensively discussed by [42,43,44]. Validation model Eqs. (9–12) have been presented below. The error statistics interpretation can be seen in Table 10. In addition, Eqs. (13–15) were used to predict the power consumption, air temperature, relative humidity, and chilled water temperature at the various CWTS and Eq. (16) for calculating the Coefficient of Performance (COP).

$$\mathrm{MAE}=\frac{1}{n}\sum \limits_{i=1}^{n} \left|\left({Y}^{\mathrm{obs}}-{Y}^{\mathrm{sim}}\right)\right|$$
(9)

where n = number of samples used, \({Y}^{\mathrm{obs}}\) = measured parameter (from observation/ experiment), and \({Y}^{\mathrm{sim}}\) = computed from CFD simulation.

$$\mathrm{RD}=\frac{(\mathrm{Predicted}-\mathrm{Experimental})}{\mathrm{Experimental}}$$
(10)
$$\mathrm{NSE}=1-\left[\frac{{\sum }_{i=1 }^{n} {\left({Y}_{i}^{\mathrm{obs}}-{Y}_{i}^{\mathrm{sim}}\right)}^{2}}{{\sum }_{i=1}^{n} {\left({Y}_{i}^{\mathrm{obs}}-{Y}_{i}^{\mathrm{mean}}\right)}^{2}}\right]$$
(11)

where \({Y}_{i}^{\mathrm{obs}}\) = ith observation/ experiment, \({Y}_{i}^{\mathrm{sim}}\) = ith simulated value, \({Y}_{i}^{\mathrm{mean}}\) = mean of observed data, and n = total number of observations.

$$\mathrm{PBIAS}=\left[\frac{{\sum }_{i=1}^{n} \left({Y}_{i}^{\mathrm{obs}}-{Y}_{i}^{\mathrm{sim}}\right)\times 100}{{\sum }_{i=1}^{n} \left({Y}_{i}^{\mathrm{obs}}\right)}\right]$$
(12)

where \({Y}_{i}^{\mathrm{obs}}\) = ith observation/ experiment, \({Y}_{i}^{\mathrm{sim}}\) = ith simulated value, and n = total number of observations

$$ {\text{Power }}\;{\text{consumption}} = - 0.1107\,\left( {{\text{CWTS}}} \right)^{2} + \, 2.088\,\left( {{\text{CWTS}}} \right) + 78.029 \, R^2 = 1 $$
(13)
$$ {\text{Air}}\;{\text{temperature}} = 0.0627\left( {{\text{CWTS}}} \right)^2 - 1.054\left( {{\text{CWTS}}} \right) + 28.353 \, R^2 = 1 $$
(14)
$$ {\text{RH}} = 0.0457\left( {{\text{CWTS}}} \right)^2 + 0.5565\left( {{\text{CWTS}}} \right) + 49.368 \, R^2 = 1 $$
(15)
$$ {\text{COP}} = \frac{{{\text{Chiller}}\;{\text{ cooling}}\;{\text{ capacity}}\,{ }({\text{kW}})}}{{{\text{ Power}}\;{\text{ consumption}}\,{ }({\text{kW}})}} $$
(16)
Table 10 Error statistics interpretation.
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5 Results and Discussion

5.1 Effects of Chilled Water Temperature Setpoint on Power Consumption

Chilled water flowing through the fan coils (copper coils) absorbs heat from the air through convective cooling. The descriptive statistics of the chiller systems’ power consumption at three different chilled water temperature setpoints (CWTS) 10 °C, 12.5 °C, and 14 °C are summarised in Table 11. The mean highest power consumption for the chiller, pump, and fan coil unit is 77.40 kW, 9.75 kW, and 0.69 kW, respectively, recorded at 10 °C CWTS. The CWTS at 10 °C yielded higher power consumption among the chiller components (chiller, fan coil unit, and pump) while the least power consumption was recorded when the CWTS was set to 14 °C. The combined mean total power consumption was 87.842 kW, 86.837 kW, and 85.575 kW for the chiller system at 10 °C, 12.5 °C, and 14 °C, respectively.

Table 11 Chiller components’ power consumption at 10 °C, 12.5 °C, and 14 °C chilled water temperature setpoints
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It is evidenced from the presented results that CWTS at 10 °C and 14 °C yielded the maximum and minimum power consumption, respectively. The minimum power consumption could result from the slight difference between the indoor and ambient temperature and humidity. Since the workload of the chiller system which include cooling and dehumidification is less, the system requires less energy to maintain the indoor air for comfort. Which results in significant reductions in energy consumption. The power consumption at the various CWTS indicates that the selection of a particular CWTS could influence the energy consumed by the chiller system. Furthermore, it is observed in Fig. 8 that the lowest CWTS of 10 °C recorded the highest power consumption of 90.14 kW in an hour as against 12.5 °C which yielded 87.45 kWh, and the 14 °C, which registered the minimum power consumed per hour of 86.54 kW. The results confirmed that the higher the CWTS, the lower the power consumed will be (increasing the CWTS from 12.5 to 14 °C). Conversely, the results from Fig. 8 show a trend of approximately minus 2% change in energy consumed between the default setting of 12 °C and the reset of 14 °C. This means that a 12% increase in the CWTS reduces energy consumption per hour by 2%. According to the findings, the chiller might be operated at a higher CWTS to save energy, which is in line with Sustainable Development Goal 13 [44] (reduction of indirect emissions of the cooling sector) and backs up the assertion made by Albatayneh et al.[45] that when higher indoor temperatures are tolerated by occupants, a reduction in cooling energy use and operating cost occurs.

Fig. 8
figure 8

Energy consumption, percentage change to time by the chiller system

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5.2 Energy Consumption of Chiller System and Cost

The energy consumed and its associated cost by the chiller system is shown in Fig. 9. The total simulation time is nine (9) hours and twenty (20) minutes. The chiller works during the day’s work period from 7:00 AM to 4:20 PM. The various CWTS (10 °C, 12.5 °C and 14 °C) recorded 90.14 kWh at the cost of $ 15.32 for 10 °C, 87.45 kWh at $ 14.87 for 12.5 °C and 86.54 kWh at $ 14.71 for 14 °C. The former was the most expensive, which could be due to its high energy consumption. It should be noted that the 10th-hour reading was taken at one-third of the hour, which was 4:20 PM, and it was the last data recorded for the day. The energy consumed by the chiller system at various CWTS throughout the operational period showed variations as influenced by the time of the day [46]. These variations could stem from the occupancy rate and the prevailing weather condition at the experimental location. The total maximum cost of energy consumed by the chiller system was $ 149.33 at 10 °C CWTS per operational day, followed by $ 147.62 at 12.5 °C CWTS per operational day. The minimum total cost of energy consumed per operational day was $ 145.48 at 14 °C CWTS. This indicates that reducing CWTS could have a huge fee on the building's energy use. It also demonstrates that higher CWTS has a positive influence on the energy efficiency of the building, which is in line with Ghana's goal in the fight against climate change, which includes a transition of the refrigeration and air-conditioning (RAC) sector to climate-friendly technologies, as stated in Ghana's Intended Nationally Determined Contributions (INDC, 2015). Resetting the CWTS from 12.5 to 14 °C will turn the chiller into an energy-efficient appliance, allowing Ghana to achieve many other goals, including accomplishing Sustainable Development Goal 7 (Affordable and clean energy) [47]. However, this computed operational day cost is likely to increase or reduce based on the period of the year, the installed location, occupancy rates, and technical faults.

Fig. 9
figure 9

Energy consumption and cost of energy consumed to time by the chiller system

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5.3 Numerical Modelling Using Computational Fluid Dynamics (CFD) and ASHRAE-55 Thermal Comfort Modelling Approach

5.3.1 Grid Independence Test

A grid independence test was conducted to improve the numerical results by using successively smaller element sizes for the computation. The test was conducted by varying the mesh element statistics between 2,041,985 and 8,059,123. All numerical solutions converged for the various element sizes. Grid independence test results in Fig. 10 show that numerical stability was reached after 200,000 elements with no significant change in room temperature. Based on the grid independence test results and computational cost, a mesh element statistic of 8,059,123 was chosen for the simulation.

Fig. 10
figure 10

Grid independence test

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5.3.2 Comparative Analysis of Indoor Environment Temperature

A plot of indoor environment temperature for the experimental and predicted (CFD modelling) at the various Chilled water temperature setpoints (CWTS) is presented in Fig. 11. The analysis of the results showed that the experimental and predicted results were within the range perceived as comfortable by ASHRAE Standard 55 (2017). Indoor environment temperatures predicted by performing CFD analysis are compared with those obtained from experiments conducted at the various CWTS (10 °C, 12.5 °C, and 14 °C). Planar and three-dimensional contour plots of indoor environment temperature from the CFD modelling showing room occupants are shown in Figs. 12 and 13. It can be noticed from Figs. 12 and 13 that, the glass window region yielded the highest temperatures (about 50 °C) which is consistent with the field observation during the data collection period as the sun rays are directly incident on the glass window. Aside from the glass window region, the occupants had the next highest temperature of 37 °C (the temperature of a healthy human) in the room. Both contour plots show uniformly distributed indoor environment temperatures which are best for indoor thermal comfort. This uniform distribution in indoor environment temperatures corroborates with the results presented in Fig. 11. However, the temperature contour changes in the body figures for all configurations are mainly attributed to the different chilled water temperature setpoints considered for the study (10 °C, 12.5 °C, and 14 °C). The results suggest that the uniform distribution of indoor environmental parameters by the chiller might not be affected by the variation in CWTS.

Fig. 11
figure 11

Indoor environment temperature for the experimental and predicted (CFD simulation) at the various CWTS

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Fig. 12
figure 12

Planar contour plot of indoor environment temperature from the CFD simulation showing room occupants with the window region (highest measured temperature) highlighted in broken rectangles

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Fig. 13
figure 13

Three-dimensional planar contour plot of indoor environment temperature from the CFD simulation showing the room occupants

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However, the initial overshoot of the room temperature notice in Fig. 11 may be a result of abrupt differences in temperature due to occupancy rate, the use of heat-generating devices such as laptops inter alia, and hot meals being brought into the rooms. Infiltration could potentially be the cause as a result of the glass not being as tightly sealed as it should have been. Also, it can be seen that the predicted temperatures immediately drop from the initial value (26 °C) within a few minutes as compared to the experimental behaviour which declination is slower. The disparity may be attributed to the following reasons: (a) Between 7:00:00 AM and 8:00:00 AM the room is opened up (door and windows are opened) for cleaning purposes and to allow air change. This may be the possible reason for the sharp increase in room temperature shortly after the chiller system was started. (b) The “Driver’s office” which was used as the test room was accessed from different periods of the day (i.e., drivers entering and exiting the room) resulting in the slower declination. The aforementioned scenarios were not considered in the CFD modelling. The room was assumed to be closed throughout the simulation hence the immediate drop from the initial temperature value (26 °C) within a few minutes.

Again, the Solar Load model was used to simulate the prevailing weather conditions (solar radiation) of the test area. This model is an approximate representation of the actual prevailing solar radiation in the test area. Notwithstanding, the relative difference (RD) values obtained for the predictions for all CWTS studied fall between 0.00 and 9.07% of the corresponding experimental values, with a maximum average RD value of 3.22%. The relative difference for 10 °C CWTS was between 0.00 and 9.07% with an average RD of 3.22%. 12.5 °C CWTS relative difference ranged between 0.00 and 7.69% with an average RD of 1.71%. Furthermore, the 14 °C CWTS had an average RD of 1.15% and fell within the range of 0.00% and 6.41%. Generally, considering the range of RD values, the CFD model could be described as reasonably good. It can be used to compare indoor environmental characteristics for chiller systems and subsequently serve as a basis for thermal comfort optimisation studies.

5.3.3 Model Validation Results

The error statistics computed for the study are shown in Table 12. Nash–Sutcliffe efficiency (NSE) results were − 0.32, 0.01, and − 0.23 for 10 °C, 12.5 °C, and 14 °C CWTS. All NSE results show very good performance ratings. The mean absolute error (MAE) computed was 2.39 °C, 1.31 °C, and 0.92 °C for 10 °C, 12.5 °C, and 14 °C CWTS. From the PBIAS results shown in Table 12, the performance rating for all CWTS was very good. The performance rating for the various CWTS using NSE, MAE, and PBIAS indicate that the CFD modelling technique is good and can be used for thermal comfort modelling and design improvements.

Table 12 Error statistics
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5.4 Effects of Chilled Water Temperature Setpoint on Thermal Comfort

Indoor environmental health is very essential in Chiller design. The occupants in an enclosed environment (in this case indoor room) could suffer from discomfort and serious health complications if the indoor environment is not well managed. Occupants in an indoor environment may be exposed to the following: temperature variations, relative humidity variations, carbon dioxide concentration, particulate matter, bacteria, viruses (e.g. coronavirus), as well as other gases (carbon monoxide, hydrogen sulphide, and ammonia) [48]. Figure 14 presents the indoor temperature and relative humidity against time at 10 °C, 12.5 °C, and 14 °C chilled water temperature setpoints and at mean face velocities of 1.9 m/s, 2.1 m/s, and 2.2 m/s, respectively, at the outflows. From Fig. 14, all the various CWTS registered a mean indoor temperature value ranging between 24 and 26 °C. However, the measured mean indoor relative humidity was slightly higher (in the range between 59 and 67%) during the chiller operational hours at all the respective CWTS. The relative humidity and temperature varied with respect to the CWTS and the time of the day. This could be a result of the hot humid climatic conditions experienced at the test site (Takoradi environment). Hot humid are characterised by high temperatures and relative humidity levels [22]. That notwithstanding, indoor relative humidity between 30 and 70% does not affect thermal comfort [49]. This supports the claim made by Yun [18] that air temperature is a significant component of thermal comfort.

Fig. 14
figure 14

Indoor temperature and relative humidity against time

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To evaluate the thermal comfort conditions in the test room, the PMV-PPD was estimated using the average relative humidity and temperature measurements, as well as clothing insulation rate, metabolism rate, and air velocity values acquired from literature depending on the work type and clothes worn by occupants. For the various CWTS (10 °C, 12.5 °C, and 14 °C), the mean relative humidity and indoor temperature values for the comfort zone, as well as air movement on the psychrometric chart, are presented in Figs. 15 and 16 and Tables 13 and 14. At CWTS of 10 °C, the PMV was computed as − 0.40 (neutral) which translates to a PPD of 8%. A PMV of − 0.05 (neutral) corresponding to 5% was calculated at CWTS of 12.5 °C. Also, a PMV of 0.29 (neutral) was calculated at CWTS of 14 °C which corresponds to a PPD of 7%. According to ASHRAE 55-2020 standard [50], the PPD and PMV indices indicate that thermal comfort conditions were within the standard's prescribed limitations (below 10% and in the range of − 0.5, 0, or + 0.5, respectively) and hence were acceptable. Figures 15 and 16 also demonstrate the acceptable ranges of relative humidity and air temperature for the office. The shaded area, according to the ASHRAE 55 standard, depicts the comfort zone limits where the PMV ranges from − 0.5 to 0.5, and the red circles represent the environmental conditions according to the measurements. As shown in Table 13, the PMV showed an increasing tendency when the CWTS is increased, whereas the PPD showed a curve trend which is evident in Fig. 17. This is in line with Amoabeng et al. [22] and [33] who also demonstrated the PPD as a curve. Furthermore, the findings as shown in Table 14 revealed that all of the CWTS fall within the thermal comfort zone at 0.1 m/s airspeeds, but extending the airspeed to 0.4 m/s would cause all of the CWTS (except CWTS of 14 °C) to fall outside the comfort zone. The findings of this study corroborate those of Albatayneh et al. [45], who discovered that the PMV model is best for analysing thermal comfort in air-conditioned buildings.

Fig. 15
figure 15

Mean indoor relative humidity and temperature values to the air movement and the comfort zone on the psychrometric chart at CWTS 10 °C (a) and 12.5 °C (b)

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Fig. 16
figure 16

Mean indoor relative humidity and temperature values to the air movement and the comfort zone on the psychrometric chart at CWTS 14 °C

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Table 13 Summary of indoor thermal condition
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Table 14 Summary of indoor thermal conditions with varied air speed
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Fig. 17
figure 17

Relationship between power consumed, PPD, and COP

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5.5 Predictions of Thermal Comfort and Energy Efficiency Metrics

The thermal comfort (air temperature, relative humidity, and PPD) and energy efficiency (Power consumption and COP) metrics for the test room and chiller system were considered. The goal is to predict the CWTS that improves the efficiency of the chiller system for both energy savings and thermal comfort.

Quadratic regression models were developed for the prediction of the Power Consumption, air temperature, and relative humidity based on the Chilled water temperature setpoints (as presented in Eqs. (13–15)) with a goodness of fit value of R2 = 1. The R-squared value demonstrates a strong relationship between the CWTS, power consumption, air temperature, and relative humidity. The COP can be used to assess the energy efficiency of an air-conditioning system. Therefore, it is used in this study to assess how effectively the chiller system converts energy. The plot of the power consumption, COP, and PPD in the test room is shown in Fig. 17. It makes the tension between the two objective functions (power consumption and thermal comfort) very evident. It can be seen that from 10 to 15 °C, the PPD of the room was within the comfort zone (from 5 to 9%) with reductions in power consumption (from 87.84 to 84.4 kW) and an increase in COP.

However, with a further increase in CWTS (from 16 °C CWTS upwards), the room's PPD steadily increased from 12 to 24% but with a decrease in power consumption. Thus, with all other variables (air velocity, clothing insulation, and metabolic rate) held constant, the increase in air temperature and relative humidity values will cause the PPD and COP to increase but will cause a decrease in power consumption as can be seen from the results. A higher COP means a higher Chiller efficiency. This result is in agreement with [9] who indicated that raising the chilled water temperature does not affect the chiller system. Thus, the CWTS could be reset between 14 and 15 °C to reduce energy consumption and maintain thermal comfort.

6 Conclusions

The energy efficiency potential for an existing chilled water fan coil system has been studied in this work. Following are the study's key conclusions:

  1. 1.

    The findings indicated that the CWTS could be reset between 14 and 15 °C to reduce energy consumption and maintain thermal comfort.

  2. 2.

    The experimental findings showed that power consumption decreased with higher CWTS. In comparison, power consumption at 10 °C CWTS was 87.842 kW as 14 °C CWTS recorded the lowest (85.575 kW).

  3. 3.

    However, the chiller energy savings increased when operated at higher CWTS relative to the default. The hourly energy cost of 2% could be saved in this regard.

  4. 4.

    The study also revealed that for CWTS of 10–14 °C, thermal comfort conditions can be fairly the same at 0.1 m/s airspeed.

  5. 5.

    Apart from 14 °C CWTS extending the air velocity to 0.4 will cause discomfort indoors.

  6. 6.

    Comparing measured data to the CFD simulation results for the three different CWTS, the maximum relative difference is 9.07%. The simulation model is therefore validated and could be used to compare the indoor environmental characteristics of chiller systems.

  7. 7.

    Additionally, modelling the comfort indices during a 9-h period for each CWTS, the mean PMV value varies between  − 0.25 and 0.14 and the PPD index has values in the range of 5–6%. The PPD and PMV indices indicate that thermal comfort conditions were within the standard's prescribed limitations and hence were acceptable [28].

  8. 8.

    Also, with an increase in CWTS (from 16 to 18 °C CWTS), the room's PPD steadily increased from 12 to 24%.

  9. 9.

    The results confirm that raising the chilled water temperature increases the COP of the chiller.