Development of Mixing Temperature Prediction Model for Single-Duct Variable Air Volume System Using CFD

Abstract

The purpose of this study was to determine the annual energy consumption that can be attributed to heating, ventilation, and air conditioning (HVAC) systems’ mixing temperature error. To develop a mixing temperature prediction model for a single-duct variable air volume (VAV) system, the mixing temperature was measured using 15 temperature sensors installed in an HVAC mixing chamber as well as the existing air handling unit’s (AHU) mixing temperature sensor. The mixing chamber was modeled using computational fluid dynamics (CFD), and a coefficient of variation of the root-mean-square error of 7.927% indicated that the model was reliable. Next, CFD simulation cases were formulated, and the temperature distribution of the mixing chamber was analyzed. This revealed that the amount of outdoor airflow input and the change in the temperature distribution of the mixing chamber were directly proportional to each other and that the mixing temperature measurements for the mixing chamber were not accurate. The mixing temperature prediction model was developed through multiple regression analysis and was successfully applied and verified. Compared with the measurements provided by existing mixing temperature sensors, the mixing temperature prediction model indicated an absolute error of 0.008–0.42 °C, confirming the model’s prediction performance.

1. Introduction

With consistent economic growth and industrial development, energy usage and greenhouse gas emissions continue to increase in all sectors, and buildings account for the largest share in this regard. To save energy, the government of South Korea is promoting energy conservation standards for buildings, a housing performance labeling system, a building-specific energy efficiency rating system, and a green building certification system [1]. Of the total energy consumption in buildings, more than 45% is consumed by heating, ventilation, and air conditioning (HVAC) systems [2].

The function of the mixing chamber installed in the air handling unit (AHU) is to mix outdoor air (OA) and return air (RA). While the mixing of the two types of airs is generally assumed to be perfect, in reality, incomplete mixing occurs inside the mixing chamber [3]. This causes errors in the mixing temperature measurement. Most mixing chambers have only one mixing temperature sensor inside them, which makes it difficult to measure the exact mixing temperature [4]. Therefore, we conducted a preliminary experiment to check the mixing temperature errors that occur during the operation of the AHU. For this, 15 thermocouple sensors were equally spaced and installed inside the mixing chamber to check the mixing temperature errors obtained with the existing mixing temperature sensor found inside the mixing chamber. The thermocouple-measured mixing temperature shown in Figure 1 indicates the average temperature measured by the 15 thermocouples. The average error between the average thermocouple-measured mixing temperature and the temperature measured by the building automation system’s (BAS) mixing temperature sensor was about 2.438 °C.

As demonstrated by the results of the preliminary experiments, if the mixing temperature sensor is installed at a specific location inside the mixing chamber, the mixing temperature reading is based on the temperature at that location, resulting in a difference from the actual mixing temperature. In addition, it is not economically viable to install and operate multiple sensors to increase the accuracy of the mixing temperature measurement [5]. Thus, mixing temperature measurement errors are caused based on the installation location and number of mixing temperature measurement sensors inside the AHU. These errors can affect the automatic operation of the AHU system and the annual energy usage of the cooling and heating coils.

Recently, various studies have been conducted to improve the energy efficiency and energy saving of buildings through efficient operation of HVAC systems, and it is an important topic. Ahn presented a method for predicting an AHU’s supply air temperature using machine learning-based automation algorithms (AutoML). By optimizing various machine learning models through AutoML (Auto-Sklearn) and comparing them with existing artificial neural network (ANN) models, Ahn found a 0.03% to 1.16% higher accuracy [6]. Kim used TRNSYS to analyze the impact of mixing temperature sensor error in AHU on cooling energy requirements during economizer control. The error of the existing mixing temperature sensor measured through experiments was about −0.3~0.5 °C and it was found that up to about 10,000 MJ of additional cooling energy was required depending on the mixing temperature setting. The mixing temperature correction improved the measurement performance of the existing mixing temperature sensor, and the comparison of the amount of outdoor airflow input confirmed that up to 400CMH of additional outside air input was required, so further research is needed, including on the optimal installation location of the mixing temperature sensor and the development of a virtual mixing temperature sensor [7]. In order to prevent indoor discomfort and energy waste due to fixed setpoints when controlling the outdoor airflow cooling of an AHU system, Lee developed an algorithm for controlling the mixing temperature setpoint of an outdoor airflow cooling system using a prediction model and saved about 18% energy compared to the existing method [8]. As such, mixing temperature measurement is important in AHU systems and errors in mixing temperature measurement cause problems with system operation and energy consumption. Previous studies have proposed various approaches for efficient operation and energy saving of AHU systems, but further research is needed in terms of the accuracy of mixing temperature measurement and prediction. This study aims to develop a mixing temperature prediction model that can respond to various variables and improve the reliability of the system through sensor error compensation.

This study was conducted in three steps, as shown in Figure 2, to develop a mixing temperature prediction model for the mixing chamber.

(1)

Step 1: Boundary condition data were collected and analyzed to model the mixing chamber using computational fluid dynamics (CFD). The data collection method utilized BAS data based on field experiments, experimental measurement data, and data from the South Korean meteorological administration to determine boundary conditions. Return airflow, return temperature, outdoor airflow, and outdoor temperature were set as the boundary conditions to check the temperature inside the mixing chamber. The real-time temperature values were obtained from the BAS data, and the temperature distribution and airflow values inside the mixing chamber were collected from the measurement data obtained through field experiments. In addition, to accurately verify the outdoor temperature values, they were compared with data from the South Korean meteorological administration, and seasonal outdoor temperature data were collected. Based on the collected data, the return airflow, return temperature, outdoor airflow, and outdoor temperature were set as the input boundary conditions for CFD modeling.

(2)

Step 2: In this step, simulations were carried out by substituting the boundary conditions, and the temperature distribution results obtained through the modeling process and those of the actual data were compared to evaluate the reliability of the model. This reliability evaluation approach was based on the criterion that a coefficient of variation (CV) of the root-mean-square error (RMSE) of less than 30% is considered reliable according to Guideline 14 of the American society of heating, refrigerating and air-conditioning engineers (ASHRAE) [9]. After the reliability evaluation, a total of 60 CFD simulation cases were tested according to return airflow, return temperature, outdoor airflow, and outdoor temperature to develop a mixing temperature prediction model.

(3)

Step 3: CFD simulations were carried out according to each case to derive the mixing temperature, and the mixing temperature prediction model was proposed. In addition, the mixing temperature prediction model was applied to the actual system and the mixing temperature prediction model was verified.

A mixing temperature error prediction model that employs CFD simulation was developed and proposed in this study to reduce unnecessary energy wastage in the operation of AHUs.

2. Methodology

In this research, CFD was used to develop an AHU mixing temperature prediction model utilizing return airflow, outdoor airflow and outdoor temperature. CFD is a tool for analyzing and predicting complex thermal fluid flow phenomena and is based on the governing equations of a continuous fluid that basically satisfy the laws of the conservation of mass, momentum and energy [10]. These governing equations are often represented by the Navier–Stokes equations, which are partial differential equations that describe the behavior of a fluid and the physical phenomena associated with it. In CFD, such partial differential equations are converted into differentiated algebraic equations that are to be solved numerically [11]. By setting the initial and boundary conditions to solve the equations, one can accurately predict the behavior of a fluid over time and space [12].

For our fluid analysis, we used the continuity equation, the Navier–Stokes equations and the energy equation to determine the heat transfer and temperature distribution. Of the aforementioned equations, the energy equation is a differential equation that represents the law of energy conservation, which refers to the time and space variation of energy in a fluid, and it is represented by Equation (1) [9].

$${\displaystyle \frac{\partial }{\partial \mathrm{t}}}\left(\mathsf{\rho }\left(\mathrm{e}+{\displaystyle \frac{{\mathrm{v}}^2}{2}}\right)\right)+\nabla ·\left(\mathsf{\rho }\mathrm{v}\left(\mathrm{h}+{\displaystyle \frac{{\mathrm{v}}^2}{2}}\right)\right)=\nabla ·\left({\mathrm{k}}_{\mathrm{e}\mathrm{f}\mathrm{f}}\nabla \mathrm{T}-\sum _{\mathrm{j}}{\mathrm{h}}_{\mathrm{j}}{\overrightarrow{\mathrm{J}}}_{\mathrm{j}}+{\overline{\mathsf{\tau }}}_{\mathrm{e}\mathrm{f}\mathrm{f}}·\overrightarrow{\mathrm{v}}\right)+{\mathrm{S}}_{\mathrm{h}}+\nabla ·{\overrightarrow{\mathrm{q}}}_{\mathrm{r}}$$

(1)

Here, $\mathsf{\rho }$ is the density (kg/m³), $\mathrm{e}$ is the internal energy (J/kg), ${\displaystyle \frac{{\mathrm{v}}^2}{2}}$ is the kinetic energy term (J/kg), $\mathrm{v}$ is the flow velocity vector (m/s), $\mathrm{h}$ is the enthalpy (J/kg), ${\mathrm{k}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is the effective thermal conductivity (W/m·K), $\mathrm{T}$ is the temperature (K), $\nabla \mathrm{T}$ is the temperature gradient (K/m), ${\mathrm{h}}_{\mathrm{j}}$ is the enthalpy of component $\mathrm{j}$ (J/kg), ${\mathrm{J}}_{\mathrm{j}}$ is the component diffusive flux (kg/m²·s), ${\overline{\mathsf{\tau }}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is the effective viscous stress tensor, ${\mathrm{S}}_{\mathrm{h}}$ is the volumetric heat source (W/m³), and ${\overrightarrow{\mathrm{q}}}_{\mathrm{r}}$ is the radiant energy flux (W/m²).

Based on the assumption that heat transfer within a fluid or solid does not occur by conduction, this equation transform as follows:

$${\mathrm{k}}_{\mathrm{e}\mathrm{f}\mathrm{f}}=0$$

(2)

Equation (2), and only the part of Equation (1) that corresponds to enthalpy, is an expression for temperature.

In this case, the enthalpy per component is defined by Equation (3).

$${\mathrm{h}}_{\mathrm{j}}={\int }_{{\mathrm{T}}_{\mathrm{r}\mathrm{e}\mathrm{f}}}^{\mathrm{T}}{\mathrm{c}}_{\mathrm{p},\mathrm{j}}\mathrm{d}\mathrm{T}$$

(3)

Here, ${\mathrm{T}}_{\mathrm{r}\mathrm{e}\mathrm{f}}$ is the reference temperature (K), $\mathrm{T}$ is the current temperature (K), and ${\mathrm{c}}_{\mathrm{p},\mathrm{j}}$ is the specific heat of the static pressure of component j (J/kg·K).

For ideal gasses, the enthalpy $\mathrm{h}$ can be expressed according to the relationship given in Equation (4).

$$\mathrm{h}={\mathrm{c}}_{\mathrm{v}}\mathrm{T}+{\displaystyle \frac{{\mathrm{p}}_{\mathrm{a}\mathrm{b}\mathrm{s}}}{\mathsf{\rho }}}$$

(4)

Here, ${\mathrm{c}}_{\mathrm{v}}$ is the static specific heat (J/kg·K) and ${\mathrm{p}}_{\mathrm{a}\mathrm{b}\mathrm{s}}$ is the absolute pressure (Pa).

The temperature is derived using Equation (5).

$$\mathrm{T}={\displaystyle \frac{1}{{\mathrm{c}}_{\mathrm{v}}}}(\mathrm{h}-{\displaystyle \frac{{\mathrm{p}}_{\mathrm{a}\mathrm{b}\mathrm{s}}}{\mathsf{\rho }}})$$

(5)

Based on Equation (5), the mixing temperature can be calculated by setting ${\mathrm{T}}_{\mathrm{i}}$ as the temperature at a specific coordinate in the CFD simulation and ${\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{x}}$ as the average temperature at N points. This can be expressed as Equation (6).

$${\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{x}}={\displaystyle \frac{1}{\mathrm{N}}}\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{T}}_{\mathrm{i}}={\displaystyle \frac{1}{\mathrm{N}}}\sum _{\mathrm{i}=1}^{\mathrm{N}}({\displaystyle \frac{1}{{\mathrm{c}}_{\mathrm{v}}}}({\mathrm{h}}_{\mathrm{i}}-{\displaystyle \frac{{\mathrm{p}}_{\mathrm{a}\mathrm{b}\mathrm{s}}}{\mathsf{\rho }}}))$$

(6)

3. Set-Up of Test and CFD Simulation

3.1. Target Building and System

In this study, the temperature measured by the mixing temperature sensor inside the AHU was recorded in the field, and the target space was the HVAC system of the laboratory of Yeungnam University located in Gyeongsan, Gyeongsangbuk-do, South Korea. An overview of the target space is presented in

Table 1. Target building and system.

Category		Contents
Building	Location	Gyeongsan-si
	Use	Laboratory
System	HVAC	Single-duct VAV system
	Target	Mixing chamber

and Figure 3a. A single-duct variable air volume (VAV) system was installed in the laboratory, and the AHU mixing temperature could be monitored through the BAS, as shown in Figure 3b.

3.2. Data Collection for Mixing Chamber

The experiment was conducted in March 2024, which included collecting temperature data for the inside of the mixing chamber. Data Logger 34970A 4.3 (Keysight Technologie, Santa Rosa, CA, USA) was used to measure the temperature points for the inside of the mixing chamber; the equipment specifications are provided in

Table 2. Equipment specification.

Category	Contents
34970A	Scan interval	0–99 h; 1 ms step size
	Scan count	1–50,000 or continuous
GDT-420	Temperature range	−30~130 °C
	Accuracy	$\pm$0.3 °C
TMCx-HD	Temperature range	−40–100 °C in air
	Temperature error	$\pm$0.25 °C (0–50 °C reference)

. The GDT-420 was the temperature measurement sensor installed inside the mixing chamber and is shown in Figure 4a on the left side of 1A. Figure 4b displays the installation locations of the thermocouple temperature measurement on the inner cross section of the mixing chamber. In addition, the measurement point is a thermocouple installed at a distance of 150 mm from the wall. The thermocouples were installed at 15 points that were equally spaced across the cross section of the mixing chamber. Measurement points 1A–1C are the temperature measurement points where outdoor air is introduced from the top, while measurement points 3A–3C are the temperature measurement points where return air is introduced from the front. A tool was made to aid with thermocouple installation, and the thermocouples were installed as shown in Figure 4b. The storage frequency for the temperature data was set to one minute, and the data were transferred to a computer through the data logger software.

To calculate the mixing temperature based on Equation (6), we calculated the mixing temperature using Equation (7), where ${\mathrm{T}}_{\mathrm{i}}$ is the temperature for a specific coordinate in the CFD simulation based on Figure 4a, and ${\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{x}}$ is the average temperature of ${\mathrm{T}}_{\mathrm{i}(\mathrm{i}=\mathrm{1,2},3···15)}$.

$${\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{x}}={\displaystyle \frac{1}{15}}\sum _{\mathrm{i}=1}^{15}{\mathrm{T}}_{\mathrm{i}}={\displaystyle \frac{1}{15}}\sum _{\mathrm{i}=1}^{15}({\displaystyle \frac{1}{{\mathrm{c}}_{\mathrm{v}}}}({\mathrm{h}}_{\mathrm{i}}-{\displaystyle \frac{{\mathrm{p}}_{\mathrm{a}\mathrm{b}\mathrm{s}}}{\mathsf{\rho }}}))$$

(7)

Table 3. Temperature measurement results from experiments.

	Row	A	B	C
Column
1		15.954	15.536	16.151
2		20.002	20.206	20.587
3		22.426	22.802	21.991
4		22.138	22.356	21.843
5		21.326	21.621	21.001

presents the results of measuring the temperature at the defined points inside the mixing chamber. It can be seen that the temperature measured at the top is relatively low, while that at the center is relatively high. This is because the outdoor airflow enters from the top, and the return airflow from the center.

3.3. Overview of CFD Simulation

3.3.1. Boundary Condition

Ansys Fluent 24.1, a CFD program, was used to develop a mixing temperature prediction model for a single-duct VAV system. The modeling was implemented as 450 mm × 450 mm for the outdoor air cross section, 1200 mm × 400 mm for the return air cross section, 1400 mm × 1000 mm for the exit cross section, and 2000 mm for the exit length. As boundary conditions for the reliability verification, the boundary conditions obtained through the experiment were used: an outdoor airflow of 483.41 CMH and outdoor temperature of 10.833 °C, and a return airflow of 522.4 CMH and return temperature of 24 °C. For CFD simulation, the mixing chamber was modeled in three dimensions using SpaceClaim 24.1. Next, Fluent Meshing was used to form the grid for the simulation before Fluent Solution was used to run the simulation with the boundary conditions. As shown in Figure 5a, the grids were polyhedral, with a maximum size of 20 mm. Figure 5b is a 3D model of a mixing chamber. The number of lattices was modeled to be about 2,000,000, and the simulation cross section was A-A’. The CFD simulation conditions were governed by the pressure-based solver, which solved the subsonic range as shown in

Table 4. CFD boundary conditions.

Category	Factor
Solver type	Pressure-based
Solver time	Steady
Energy	On
Viscous	Standard k-ε

. The gravity value was set and the simulation was performed in the steady state. The humidity was not considered and the turbulence model was solved using standard k-ε [13,14]. The convergence criterion was set based on the residual value of each calculation step and was set to $1\times {10}^{-3}$ or less for continuous equations, X-Y-Z velocity, k and ε, and $1\times {10}^{-6}$ or less for energy.

3.3.2. Verification of the CFD Simulation Model

The physical geometry of the mixing chamber was reproduced through CFD modeling to set the initial boundary conditions, and the quality of the lattice was ensured before proceeding with the simulation. To evaluate reliability, the temperature values measured through experiments at a total of 15 points evenly spaced across the internal cross section of the mixing chamber were compared to those for the same 15 points in the CFD simulation. The experiments were performed with the outdoor air damper opening rate set to 30%, and

Table 5. Temperature measurement results from experiments and CFD simulations.

	Row	A	B	C
Column
1	Experiment (°C)	15.954	15.536	16.151
	CFD (°C)	17.234	18.561	18.214
	Absolute error (°C)	1.280	3.025	2.063
2	Experiment (°C)	20.002	20.206	20.587
	CFD (°C)	16.792	19.139	19.430
	Absolute error (°C)	3.210	1.067	1.157
3	Experiment (°C)	22.426	22.802	21.991
	CFD (°C)	22.156	24.015	20.224
	Absolute error (°C)	0.27	1.213	1.767
4	Experiment (°C)	22.138	22.356	21.843
	CFD (°C)	21.078	20.782	21.794
	Absolute error (°C)	1.060	1.574	0.049
5	Experiment (°C)	21.326	21.621	21.001
	CFD (°C)	19.652	22.145	20.825
	Absolute error (°C)	1.674	0.524	0.176

presents the comparison of the temperature error rate between the experimental set-up and CFD simulation for the interior temperature of the mixing chamber. On comparing the experimental and the CFD simulation results, it was found that there was a maximum absolute error of 3.210 °C and that the average absolute error was 1.341 °C.

A prediction model is considered reliable when the CV (RMSE) of the model prediction and the actual measurement is less than 30%, as defined by ASHRAE Guideline 14. This is represented by Equation (8). The CV (RMSE) value for the prediction model developed in this study is 7.927%, thus proving that the CFD modeling can be considered reliable.

$$\mathrm{C}\mathrm{V}(\mathrm{RMSE})=\sqrt{{\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{y}}_{\mathrm{i}}-{\dot{y}}_i{)}^2}{\mathrm{n}}}}/{\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\dot{y}}_i}{\mathrm{n}}}$$

(8)

Here, ${\mathrm{y}}_{\mathrm{i}}$ is the simulation prediction, ${\dot{y}}_i$ is the actual measurement, and $\mathrm{n}$ is the amount of data.

3.4. CFD Simulation Cases

The aim of this study was to develop a mixing temperature prediction model, which was carried out using Ansys Fluent 2024 R1. The simulation case employed for the development of the prediction model was determined after the return temperature was fixed at 24 °C, and the mixing temperature prediction model was presented and verified after the CFD simulation of the cases was carried out according to return airflow, outdoor airflow and outdoor air temperature. Figure 6 categorizes the CFD simulation cases according to return temperature, return airflow rate and outdoor air temperature. The return temperature was kept constant at 24 °C, while the outdoor air temperature was set using seasonal temperature data. For the airflow, the damper opening rate was calculated based on the requirement of 70% return air and 30% outdoor air, and the outdoor airflow was calculated based on the return airflow using the law of the conservation of mass, which is represented by Equation (9). The range for the return airflow was divided into 100CMH steps to set the airflow conditions from 100 to 1000CMH. The CFD simulation was performed by setting boundary conditions according to these airflow conditions.

$${\mathrm{Q}}_{\mathrm{O}\mathrm{A}}={\mathrm{Q}}_{\mathrm{R}\mathrm{A}}\times {\mathsf{\alpha }}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}$$

(9)

Here, ${\mathrm{Q}}_{\mathrm{O}\mathrm{A}}$ is the outdoor airflow (CMH), ${\mathrm{Q}}_{\mathrm{R}\mathrm{A}}$ is the return airflow (CMH), and ${\mathsf{\alpha }}_{\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}}$ is the ratio of the return and outdoor air damper opening rates (0.429).

4. Result and Discussion

4.1. Temperature Distribution in the Mixing Chamber

The measurement points used in the CFD simulation were set to be the same as those used during the experiments to extract the data. Figure 7 displays a heat map of the temperature distribution for each CFD simulation case. Figure 8 shows a graph that presents the temperature data from Figure 7 in the form of a boxplot. It can be seen that the temperature distribution in Cases 5, 11, 17, 23, 29, 35, 41, 47, 53, and 59, which are cases where the outdoor air temperature and the temperature of the air entering the mixing chamber were similar, tends to narrow. This indicates that the smaller the difference between the outdoor air temperature and the airflow temperature, the more uniform the temperature distribution inside the mixing chamber. Conversely, the larger this temperature difference is, the wider the temperature distribution in the mixing chamber would be, which can affect the measurement of the AHU’s mixing temperature sensor. If the airflow rate in the mixing chamber is high, the mixing temperature tends to decrease when the outdoor air temperature decreases, whereas the mixing temperature increases when the outdoor air temperature increases. The mixing temperature derived from the CFD simulations was used as the average value of the temperature measured at the 15 points.

4.2. Prediction of Mixing Temperature

It was confirmed through experiments that the mixing temperature error occurs due to the use of the existing mixing temperature sensor of the AHU. Therefore, the average temperature values for the return airflow, outdoor airflow, outdoor air, and CFD simulation data of each case were used to develop the mixing temperature prediction model. Multiple regression analysis was performed, and the independent variables were return airflow, outdoor airflow and outdoor air temperature, while the dependent variable was the mixing temperature. The prediction model for mixing temperature is represented by Equation (10).

$${\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{x}, \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{t}}=203.827{\mathrm{Q}}_{\mathrm{R}\mathrm{A}}-475.603{\mathrm{Q}}_{\mathrm{O}\mathrm{A}}+0.42{\mathrm{T}}_{\mathrm{O}\mathrm{A}}+15.366$$

(10)

Here, ${\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{x}, \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{t}}$ is the prediction model’s mixing temperature (°C), ${\mathrm{Q}}_{\mathrm{R}\mathrm{A}}$ is the return airflow (CMH), ${\mathrm{Q}}_{\mathrm{O}\mathrm{A}}$ is the outdoor airflow (CMH) and ${\mathrm{T}}_{\mathrm{O}\mathrm{A}}$ is the outdoor air temperature (°C).

4.3. Verification of the Mixing Temperature Prediction Model

To validate the mixing temperature prediction model, we compared the AHU mixing temperature sensor data, the thermocouple data, and the mixing temperature prediction model results. Based on the data obtained from the field experiment of the automatically controlled HVAC system in the laboratory of Yeungnam University, the mixing temperature prediction model expression was substituted into Equation (10).

Table 6. Mixing temperature prediction model validation.

Case	Return Airflow (CMH)	Outdoor Airflow (CMH)	Outdoor Temp. (°C)	HVAC Mixing Temp. (°C)	Prediction Model Temp. (°C)	Absolute Error (°C)
A	574.56	246.24	29.3	26.000	26.030	0.030
B-1	635.04	272.16	29	25.800	25.732	0.068
B-2			29.3	26.000	25.858	0.142
B-3			29.4	26.000	25.900	0.100
C-1	665.28	285.12	29.1	25.700	25.687	0.013
C-2			29.5	25.900	25.855	0.045
C-3			29.8	26.100	25.981	0.119
D	725.76	311.04	29.8	26.100	25.808	0.292
E	816.48	349.92	30.4	26.100	25.801	0.299
F	876.96	375.84	32.2	26.300	26.384	0.084
G	907.20	388.8	32	25.900	26.214	0.314
H-1	937.44	401.76	32.7	26.000	26.422	0.422
H-2			32.8	26.400	26.464	0.064
I	967.68	414.72	32.7	26.400	26.335	0.065
J-1	1058.40	453.6	32.3	25.900	25.908	0.008
J-2			32.8	26.300	26.118	0.182
J-3			33.2	26.100	26.286	0.186
K	1118.88	479.52	33.1	26.100	26.071	0.029
L-1	1149.12	492.48	33.1	26.100	25.985	0.115
L-2			33.2	26.000	26.027	0.027

summarizes the cases where the difference between the thermocouple data and the mixing temperature prediction was smaller than that between the thermocouple data and the mixing temperature sensor measurements. Thus, the prediction model was validated. The absolute error between the existing mixing temperature sensor and the mixing temperature prediction model was found to be as low as 0.008 °C and as high as 0.422 °C, demonstrating its performance with regard to predicting the mixing temperature.

5. Conclusions

In this study, 15 temperature sensors were installed inside an AHU’s mixing chamber to determine the degree of error in the AHU mixing temperature measurements through experiments and to develop a mixing temperature prediction model for a single-duct VAV system. The mixing temperature was also measured using the existing AHU mixing temperature sensor. The mixing chamber was modeled using CFD, and a CV (RMSE) value of 7.927% was obtained, indicating that the model was reliable. The CFD simulation cases were then formulated, and the temperature distribution of the mixing chamber was analyzed. From the temperature distribution acquired through the CFD simulations, it was found that the amount of outdoor air input was directly proportional to the change in the temperature distribution of the mixing chamber. Further, it was found that the temperature measured in the mixing chamber was not accurate. The mixing temperature prediction model was developed through multiple regression analysis, and field application and validation were carried out. The mixing temperature prediction model was developed through multiple regression analysis, and field application and validation were conducted. Compared to the default mixing temperature sensor, the mixing temperature prediction model yielded a low absolute error of 0.008–0.422 °C and validated the performance of the mixing temperature prediction model.

This study utilizes CFD to develop a mixed temperature prediction model by simulating various boundary conditions that are difficult to apply in real experiments. By applying the mixed temperature prediction model, it can be utilized to improve the efficiency of HVAC systems. It can also be utilized to develop a predictive control algorithm for HVAC systems by simulating various boundary conditions. This can contribute to energy savings and improved indoor air quality by monitoring the system’s mixing temperature prediction in real time and optimizing the indoor environment. But, this study evaluated the results of the mixing temperature prediction model over a short period of time. For effective future field applications of the prediction model, long-term validation is required, and it is necessary to verify the prediction model in real time in relation to the automatic control system of the AHU.