2.1. Overall Methodology
The developed methodology, presented in the flow chart (
Figure 2), includes the definition of the standardised cases used in the parametrisation of the CFD models, the HVAC system model and the 1D thermal and comfort models integrated in the overall system model.
CFD simulations of the cabin model were performed for 80 standardised cases with variations in terms of the HVAC settings, ambient temperatures and humidity. The standardised cases are reported in
Table 1 and include the most relevant scenarios for automotive heating and cooling systems. For the CFD model, only the temperatures and air velocity at distinct locations were evaluated, therefore the air humidity was neglected and set to 0%.
The simulation results from the CFD model were collected and post-processed for use in the 1D thermal model, which was implemented in the simulation environment Dymola/Modelica [
38,
39]. The CFD results were interpolated between the operating points, allowing the usage of detailed results from CFD while requiring low computational effort. In parallel, a model of the HVAC system was implemented in Dymola/Modelica. Both the 1D thermal and comfort models and the HVAC system model were implemented in the simulation platform (overall system model).
2.2. Case Study
The case study was based on the demonstrator of the EU H2020 research project QUIET, which was the Honda Fit EV. This vehicle was derived from the second-generation Honda Jazz (called “Fit” in Japan, Sri Lanka, China, and the Americas).
The Honda Fit EV was derived from the conventionally powered Honda Jazz/Fit and the HVAC system is a direct conversion from that model. The cabin of the demonstrator vehicle and the location of the corresponding air outlets can be seen in
Figure 3. Five outlets were located on the dashboard: one on the driver′s left side (VENT side), one on the passenger′s right side (VENT side), and three in the middle position (VENT and DEF). An additional four outlets were in the leg space of the driver, front passenger (FR HEAT) and back passengers (RR HEAT).
The target outlet temperature (T
in) to the vehicle cabin was adjusted by mixing hot and fresh air. The operational modes nomenclature is defined in
Table 2 and defines five different settings for the air flow distribution.
The methodology includes the development of a dataset of simulations from the CFD generic approach, in order to be optimally integrated in a 1D dynamic model, including the thermal aspects of both the vehicle cabin and the HVAC system. In order to validate the methodology, a validation case was selected, and the settings are reported in
Table 3.
The validation case measurements were taken in a climatized chassis dyno [
37] with K-type thermocouples to monitor surface temperatures in different locations (head, chest, legs) of the vehicle cabin. Additionally, comfort measurements were taken with the device FLATMAN, developed by LumaSense/Innova. The device FLATMAN is a thermal measurement mannequin with an aluminium frame, equipped with dry heat loss transducers at the representative locations.
2.3. Thermal Comfort Modelling
Thermal comfort is the condition of mind that expresses satisfaction with the thermal environment [
40]. The thermal comfort assessment in a confined space, such as a vehicle cabin, is a complex task since it involves the evaluation of both the physiological and the psychological states of the person under consideration. A well known index used to estimate the global thermal comfort of people is the predicted mean vote (PMV) index [
40], which gives the thermal comfort response in steady state for an airconditioned environment, and was originally developed for building applications. The PMV is a quantitative measure of human warmth, and a graphical representation of it is presented in
Table 4.
The index was developed based on a large statistical research study on a group of individuals and it defines the ranges that result in thermal satisfaction for most of the occupants in a confined space. A PMV value of zero represents the ideal value considered as the thermal neutrality. PMV values in the range between −1.0 and +1.0 were considered acceptable and recommended. The PMV value is calculated based on Equations (1) and (2). The PMV index is a function of four thermal environment variables and two human body factors, see
Figure 4.
The PMV index [
40] includes the factors related to thermal comfort, such as the metabolism rate (M), clothing insulation (I
cl), air humidity (RH), air temperature (T
air), radiant temperature (T
rad) and air speed (v
air):
where:
with:
M metabolic heat rate (W/m2);
W activity level (W/m
2) removed from the inputs of
Figure 4 as assumed negligible;
tcl temperature at clothes’ level (K);
pa water vapour pressure (Pa);
ta air temperature (K);
Icl thermal insulation of clothes (Clo);
fcl clothing factor (-);
tmr mean radiant temperature (K);
hc convective heat transfer (W/m2.K).
Table 5 gives an overview of the PMV factors with the typical ranges and the specific factors used for the case study.
2.4. Cabin CFD Modelling
Geometry data, provided by HONDA, were processed with SpaceClaim 3D [
41] in Ansys Fluent [
42]. The geometry model reproduces the physical properties of the vehicle cabin, including the heating and vent inlet and outlet locations and dimensions, windshield angle, and chassis parameters, which are influential to the performance of the vehicle cabin heating and cooling system. In this study, an additional four manikins were modelled. These manikins were designated as the driver and three passengers and were in a sitting posture. The material properties specified for the car compartment surfaces and the human body are listed in
Table 6. The wall properties were iteratively adapted in order to obtain comparable heat losses, as for the validation case.
The fluid flow distribution within the cabin was obtained using the commercial CFD package ANSYS Fluent [
43]. The flow is governed by the conservation equations for mass, momentum and energy. The effects of turbulence were accounted for using the Reynolds-averaged Navier-Stokes (RANS) approach (k-w SST) [
43], which ensures higher accuracy near the wall, and is therefore appropriate when simulating the maninkins [
43]. The snappyHexMesh utility [
44] was used for the generation of the mesh. Starting from the triangulated surface representation of the geometry (STL), the polyhedral mesh was generated by snapping the background mesh onto the nearest surface.
Figure 5 illustrates the meshed grid of the model for the vehicle cabin. The CFD model includes the heat transfer phenomena of conduction, convection and radiation, although radiation represents a minor effect due to the small temperature difference between the surfaces and the assumption of no solar radiation. The boundary conditions were extrapolated from experimental data.
The cabin supply air flow rate and temperature were specified at the outlet vent surfaces. The pressure outlet boundary condition used at the outlet vents was at a constant atmospheric pressure of 101.3 kPa, with the vehicle at rest. Nonslip wall conditions were imposed at the wall surfaces of the windshield, side window, rear window, dashboard, seats, and floor. The windshield, side window, and rear window were treated in the radiation equations as semi-transparent walls. To ensure the reliability of the simulated results, the CFD model was validated against the experimental data and the validation results are provided in
Section 3.
2.5. HVAC System Modelling
The HVAC system 1D model was developed based on models of the Modelica Standard Library [
39] and TIL Suite [
45]. The parameters for each of the sub-models were derived either from the available measurement data or from a technical datasheet. The system depicted in
Figure 6 consisted of three different loops: (1) refrigerant propane R290, (2) coolant with a water–glycol 50% mixture and (3) air cycle.
The HVAC system is built up in an indirect topology, which means that the thermal power provided by the refrigerant cycle is transmitted to the coolant cycle via plate heat exchangers. The coolant cycle, based on a 50% water–glycol mixture, is connected to MPET (multi-port extruded tube) heat exchangers for the condenser and evaporator, which transmit the thermal power to the air side, either to the ambient at the vehicle front or to the cabin air. The coolant valves can be used to switch between the heating or cooling operation (connecting the condenser heat exchanger to the heater core for the heating operation or the evaporator heat exchanger to the low-temperature radiator for the cooling operation). Even though direct refrigerant cycles can achieve higher system efficiencies, a coolant-based system is easier and safer to install due to the lower pressure. The refrigerant cycle, consisting of the compressor, condenser, expansion valve (TXV), internal heat exchanger (IHX) and evaporator, is based on propane as a refrigerant.
2.6. Thermal and Comfort Model and HVAC System Integration
The cabin 1D thermal model was used to calculate the cabin temperature. It was based on two thermal masses: the cabin air (assumed 2.5 m
3) and the solid cabin parts. The total thermal mass of the solid cabin parts (such as doors, steering wheel, seats, etc.) was an estimated 120 kg with a total thermal capacity of 5000 J/K, while the convective heat transfer between the air and solid parts was set to 260 W/K. The 1D thermal model considers an overall heat transfer from cabin to outside of about 36 W/K. A schematic overview of the thermal cabin model is provided in
Figure 7. The aforementioned parameters for the model were derived from the measurement data.
The cabin model exchanges data with the HVAC model and the sub-model “flowDistribution” in which the results of the CFD simulations are derived and implemented,
Figure 8. The “flowDistribution” model implements the temperature and air-velocity distribution at distinct locations in the cabin, i.e., the head, chest and legs of each of the four passengers (driver, co-driver, behind driver, behind co-driver), constituting the mean value of the entire cabin and the comfort model based on the equations presented in
Section 2.3.
The “flowDistribution” is derived from the parametric variation with the various boundary conditions as presented in
Table 7 (80 CFD simulation results).
Steady state results from the CFD simulations are implemented in the “flowDistribution” model as lookup tables (I = 1.10) and depending on the values of “Mode” and “Recirculation mode”, the corresponding (table) is retrieved:
Temperature (T
ss) and the velocity (v) at steady state conditions for all positions (j = 1.3) are obtained, linearly interpolating the values with respect to the cabin supply volume flow rate (V
in) and the cabin supply temperature (T
in):
As a next step, the actual temperature (T
actual) is calculated based on the factor (k) which is obtained from the 1D thermal model (T
cabin), the steady state mean cabin temperature (T
cabin,ss) from the CFD simulations and the ambient temperature (T
ambient):
As the temperature (T
cabin) from the 1D thermal model has a transient behaviour, the actual temperatures for the various locations of the cabin will inherit the behaviour, and namely:
The approach provides transient results from the CFD steady state conditions, contributing to a large simulation time and computational effort savings. The calculated temperatures (Tactual) and air velocities (v) at the various locations (j) were then used as inputs for the PMV model implemented in Dymola/Modelica. As a result, the PMV model gives the response to a change from an equilibrium or a steady state, thus resulting in the capability of predicting the transient behaviour for the PMV index.