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Article

Improving the Energy Efficiency of Vehicles by Ensuring the Optimal Value of Excess Pressure in the Cabin Depending on the Travel Speed

by
Ivan Panfilov
1,
Alexey N. Beskopylny
2,* and
Besarion Meskhi
3
1
Department of Theoretical and Applied Mechanics, Agribusiness Faculty, Don State Technical University, Gagarin, 1, 344003 Rostov-on-Don, Russia
2
Department of Transport Systems, Faculty of Roads and Transport Systems, Don State Technical University, Gagarin, 1, 344003 Rostov-on-Don, Russia
3
Department of Life Safety and Environmental Protection, Faculty of Life Safety and Environmental Engineering, Don State Technical University, Gagarin, 1, 344003 Rostov-on-Don, Russia
*
Author to whom correspondence should be addressed.
Fluids 2024, 9(6), 130; https://doi.org/10.3390/fluids9060130
Submission received: 29 April 2024 / Revised: 23 May 2024 / Accepted: 29 May 2024 / Published: 31 May 2024
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Abstract

:
This work is devoted to the study of gas-dynamic processes in the operation of climate control systems in the cabins of vehicles (HVAC), focusing on pressure values. This research examines the issue of assessing the required values of air overpressure inside the locomotive cabin, which is necessary to prevent gas exchange between the interior of the cabin and the outside air through leaks in the cabin, including protection against the penetration of harmful substances. The pressure boost in the cabin depends, among other things, on the external air pressure on the locomotive body, the power of the climate system fan, and the ratio of the input and output deflectors. To determine the external air pressure, the problem of train movement in a wind tunnel is considered, the internal and external fluids domain is considered, and the air pressure on the cabin skin is determined using numerical methods CFD based on the Navier–Stokes equations, depending on the speed of movement. The finite-volume modeling package Ansys CFD (Fluent) was used as an implementation. The values of excess internal pressure, which ensures the operation of the climate system under different operating modes, were studied numerically and on the basis of an approximate applied formula. In particular, studies were carried out depending on the speed and movement of transport, on the airflow of the climate system, and on the ratio of the areas of input and output parameters. During a numerical experiment, it was found that for a train speed of 100 km/h, the required excess pressure is 560 kPa, and the most energy-efficient way to increase pressure is to regulate the area of the outlet valves.

1. Introduction

In view of the active electrification and automation of transport, recently, more attention has been paid to optimizing the operation of climate control systems [1,2,3,4,5,6,7], which allows not only the obtaining of comfortable microclimate indicators, but it also reduces the energy consumption of the climate control system. The standard HVAC (heating, ventilation, and air conditioning) parameters studied include temperature and air speed [8,9,10,11,12,13,14,15,16]. Additionally, studies are carried out on air humidity, oxygen, and carbon dioxide concentrations [17,18,19,20]. Much attention is also paid to studying the movement of pollutants and pathogens [21,22,23,24]. It is known that optimizing the parameters of the climate control system affects not only the creation of comfortable conditions but also the overall energy efficiency of the vehicle. Ref. [25] simulated different vehicle ventilation strategies, mainly recirculation rate (REC), on cabin air quality and climate control system capacity. Using 70% recirculated air averaged 55% and 39% reduction in 2.5 µm particles for new and legacy filters, respectively. At the same time, an increase in recirculation increases the level of CO2 in the cabin, and its value is relevant for passengers. There is also a potential risk of windshield fogging in cold climates. Ref. [26] shows that the transport sector is committed to phasing out fossil-fuel-powered vehicles and achieving zero carbon emissions by 2050.
At the same time, one of the key tasks of research into all-electric vehicles is heating/cooling the interior, which requires a huge amount of electricity using traditional methods. HVAC optimization issues involve a systems approach, including developing new heat pump systems, ensuring adequate cabin heating/cooling, and solving existing cabin problems. Providing optimal microclimate conditions is typical for various industries [27]. The authors in [28] used the Navier–Stokes equations to create a method for predicting airborne transmission risks in bus interiors. The computational fluid dynamics analysis involved replicating complex bus cabin geometries with realistic heating, ventilation, and air conditioning. Effective strategies were proposed by the authors to prevent airborne infection.
All the listed works are devoted mainly to the study of the values of speeds, temperatures, and humidity levels of the interior space of the cabin. However, despite the large number of studies, the cited works do not pay enough attention to studying the issue of excess internal pressure, which ensures the operation of the climate system under different operating modes.
The following factors can be identified as criteria for the range of excess internal pressure:
  • The maximum pressure value should be regulated by the technological strength characteristics of the cabin body. For example, there are known cases when the cabin windows were “squeezed out” by excess pressure due to malfunctions of the outlet valves - P max .
  • Maximum pressure should be limited by sanitary requirements according to the criterion of impact on human health P r e q . An increase in atmospheric pressure of no more than 10 mmHg, or 1333 Pa, is considered harmless [29,30].
  • The lower range of values is determined by the technological features of the cabin, which consist of the presence of leaks. To prevent gas exchange and the penetration of contaminants through leaks, increased pressure is created in the cabin, which is pumped by fans of the climate system. Moreover, external pressure must be assessed not relative to atmospheric pressure, but relative to excess external pressure on the cabin body P e x t , which is formed due to resistance to vehicle movement. In particular, for railway transport in [31,32], it is stated that air pressure must be provided for control cabins of at least 15 Pa, and in passenger compartments—at least 20 Pa ( P s t d ). However, these figures require justification. Below, in this work, all designations and pressure values are given as excess pressure relative to standard atmospheric pressure.
A preliminary assessment of pressures (1) allows us to present the range of the desired value of increased pressure in the cabin P i n t as follows:
P s t d < P e x t < P i n t < P r e q < P m a x  
Simultaneously with (1), it is necessary to consider the problem of finding the real pressure P r e a l , which can be created (2) by the operation of the climate system under different operating modes:
P i n t = P o b o r
Thus, to determine the permissible values of internal pressure P i n t , it is necessary to at least determine the values: P e x t , P r e q and compare with the real pressure inside the cabin from the operation of the climate system P o b o r .
In this work, research is carried out using the example of the cabin of a mainline diesel locomotive 2TE25K [33]. To find the external air pressure P e x t , the problem of train movement in a wind tunnel is numerically considered; based on the Navier–Stokes equations, the air pressure on the cabin skin is determined depending on the speed of movement. The values of excess internal pressure P i n t , which ensures the operation of the climate system under different operating modes, are studied numerically based on the Navier–Stokes equations, and are also compared with the results of an approximate applied formula. The numerical solution of the Navier–Stokes equations is widely used for analyzing vehicle aerodynamics in research [34,35,36,37]. CFD models with large-scale grids and large time steps based on Reynolds averaging Navier–Stokes (RANS) approaches are currently popular.
Thus, the above review shows that, despite the variety of studies, insufficient attention is paid to determining the optimal pressure values in the vehicle cabin as a factor in operator comfort, as well as the energy efficiency of the power plant. The purpose of this article is to determine the optimal values of excess air pressure inside the locomotive cabin, which is necessary to prevent gas exchange between the interior of the cabin and the outside air through leaks in the cabin, including protection against the penetration of harmful substances. One is expected to study mathematical models and conduct numerical experiments to determine the values of excess pressure, as well as obtain criteria for finding the required values of these values, and also to study the influence of external air speed (vehicle speed) and operating modes of climate system configurations.

2. Materials and Methods

2.1. Governing Equations

As a physical domain, we consider the external domain of air surrounding the cabin, and the internal space of the cabin, as a continuous medium, which is a Newtonian, compressible fluid (gas). All physical quantities discussed below are considered as continuous fields depending on three-dimensional coordinates. As a mathematical model for determining the pressure outside and inside the cabin, we can consider the system of Navier–Stokes equations, consisting of the mass conservation Equation (3), momentum Equation (4), the energy Equation (5), and the Clapeyron–Mendeleev relation (6) of an ideal gas to take into account compressibility environment [38,39,40,41,42]:
∂ ρ ∂ t + ∇ · ( ρ u ) = 0 ,
∂ ρ u ∂ t + ∇ · ρ u u = ρ g + ∇ τ − ∇ p ,
∂ ρ T ∂ t + ∇ ( T ρ u ) = λ c ρ ∆ T ,
p = ρ T R M .
The main variables here are the following: u is the speed of the medium; ρ is density; p is pressure; T is temperature; τ = µ ∇ u + ∇ u T − 2 3 ∇ · u I [39], here I is the unit tensor; g is gravity.
Gas parameters: µ is viscosity; λ and c ρ are thermal conductivity and specific heat, respectively; R and M are gas constant and molar mass, respectively.
As complications and refinements of the model, diffusion equations can be added to the system of equations to take into account, for example, air humidity and gas concentrations [18], as well as a discrete model for simulating the spread of dust and pollutants, including pathogens [21].
To numerically solve the boundary differential problem (1)–(8), CFD analysis was used. This method consists of replacing the main variables with Reynolds averages [42,43,44,45,46] and using new RANS equations. In this case, additional variables and turbulence equations arise.
To obtain numerical results, the Ansys CFD [47,48] finite volume analysis software (Ansys Fluent, Release 2022 R1) was used using the k − ω turbulence model.
Thus, control Equations (3)–(6) with the necessary boundary conditions and two turbulence equations represent a closed system of equations for modeling air movement.

2.2. Application Formula for Determining Internal Pressure

To assess the reliability of the numerical model and evaluate the numerical results, an applied formula is obtained in this work. The Bernoulli Equation (7) for the flow of medium in two communicating vessels [39,40], assuming that air is an ideal nonviscous medium, can be used to estimate the amount of overpressure inside the cabin.
ρ u 1 2 2 + P 1 + ρ · g · h 1 = ρ u 2 2 2 + P 2 + ρ · g · h 2 + P r e s i s t
Here, u 1 is the average vertical speed inside the cabin, u 2 is the flow rate at the exit. P 1 —pressure in the cabin, P 2 —pressure at the cabin exit. g, h i —acceleration of free fall and height of the air column, P r e s i s t —costs of resistance and friction.
Placing P 2 = 0 at the exit from the cabin, since the absolute external pressure at the exit coincides with atmospheric pressure, and also neglecting the force of gravity for the air, we obtain from (7) a formula (8) for calculating the approximate value of the pressure inside the cabin:
P 1 = ρ u 2 2 2 − ρ u 1 2 2 + P r e s i s t .
The inlet and outlet velocities are related to each other by the following expression with the assumption of incompressibility of the flow:
u i n · S i n = u o u t · S o u t .
Here, u i n and u o u t are the speeds at the entrance and exit from the cabin, respectively, and S i n and S o u t are the areas of the entrance and exit deflectors, respectively.
To calculate the approximate value of the average vertical flow velocity for (8), one can use the formula
u 1 = S i n · u i n S c a b ,
Here, S c a b is the average cross-sectional area of the cabin.
Based on (9)–(10) and the assumption S i n ≫ S o u t , we can obtain the speed value u 1 ≪ u 2 ; therefore, the second term on the right-hand side of expression (8) can be neglected. Without taking into account the pressure loss due to air resistance and viscosity, we obtain an estimated expression for the additional pressure inside the cabin:
P 1 = P i n a p p l = ρ u o u t 2 2 .

2.3. Geometric Model

In this work, studies of pressure values are carried out using the example of a main-line freight diesel locomotive 2TE25K [33]. Figure 1 shows the appearance and geometric model for simulating the external aerodynamics of the locomotive. Figure 1a shows a photograph of the actual locomotive under study. Figure 1b shows the geometric model of the locomotive.
Figure 2 shows the cabin interior and a locomotive cabin geometric model for simulating internal fluid dynamics. Figure 2a shows a photograph of the cabin under study; Figure 2b shows a geometric model. The problem is considered symmetrical relative to the median plane; the figures below show half of the cabin with the driver.

3. Results

3.1. Numerical Analysis and Mesh Convergence

Numerical calculations were performed in the Ansys Fluent finite volume analysis package using the Pressure-Based solver using a turbulence model k − ω . The solution method was chosen by Simple.
The quality of the mesh was assessed according to two parameters (Table 1). Firstly, an assessment was carried out according to the orthogonal quality criterion. A value greater than 0.1 is acceptable [49]. Convergence was also assessed depending on the grid size; some of the data are shown in Table 1. As a result, the calculation was performed with the grid values given in the Value 2 column of Table 1.
The k − ε model can also be used; the k − ω and k − ε turbulence models are the most universal and will give similar results [49,50]. For this problem, the discrepancies are less than 1%. The reliability of the results obtained is confirmed by the use of verified numerical methods and codes in the Ansys CFD software (Release 2022 R1) product [47,48].

3.2. Numerical Results

To study the external pressure on the locomotive body, a wind tunnel was considered (Figure 3 and Figure 4). Velocity adhesion conditions were set on the bottom surface and body of the locomotive, and slip conditions were set on the upper and side surfaces. At the entrance to the wind tunnel, the speed value was set from 0 to 150 km/h, and at the exit—zero relative pressure (Table 2). The linear size of the wind tunnel was 5 locomotive lengths. It was assumed that the boundary conditions, in particular, the incoming flow rate, do not depend on time, so the problem was solved in a stationary formulation. Equations (3)–(5) allow us to solve a nonstationary problem, in particular, studying the time of stabilization of processes when starting a climate system or switching it to other modes. Such studies have also been carried out and will be added to the next work. For the stationary case, system (3)–(5) will take the following form:
∇ · ( ρ u ) = 0 ,
∇ · ρ u u = ρ g + ∇ τ − ∇ p ,
∇ T ρ u = λ c ρ ∆ T .
Figure 5 shows the velocity and pressure fields around the locomotive when moving (air blowing) at a speed of 110 km/h.
Figure 6 and Figure 7 demonstrate pressure fields around the locomotive body for a speed of 110 km/h.
As can be expected, the maximum pressure values are at the front of the cabin. It is interesting to note that in the front upper part of the housing, there is an area of vacuum (negative relative to pressure). This fact is quite important, since climate control equipment is located in the upper part of locomotives, and it is necessary to take into account the negative relative pressure in the case of air intake from vacuum points. In other words, the fan power in climate control equipment should be higher in the case of air intake from a vacuum region.
Figure 8 shows a graph of the dependence of the maximum pressure value on the locomotive body on the speed of movement. It can be seen that the pressure increases proportionally to the square of the velocity, which is consistent with the known formulas of the resistance force [37,38,39,40,41,42].
To study the values of internal pressure, the problem of internal air flow in the internal volume of the cabin was considered. Figure 4 shows the air inlet and outlet baffles. The cabin walls were set with conditions for air velocity adhesion, the inlet speed was set (red arrows in Figure 4a), and the outlet had zero relative stationary pressure (blue arrow in Figure 4b) (Table 3).
The dependence of internal pressure on the supply airflow rate and on the size of the inlet and outlet baffles was studied.
Figure 9 shows the fields of velocity and pressure values for an incoming flow velocity of 1 m/s (flow rate 950.4 m3/h). The area of the input deflectors was 0.264 m2 and the area of the output deflectors was 0.020 m2. Figure 10 shows the velocity vectors in the plane passing through the driver in normal scale (Figure 11a) and enlarged scale (Figure 11b).
To assess the flow turbulence for the above parameters of flow rate and deflector area, Figure 10 shows the turbulence intensity value [49]. According to the criterion for assessing the value of turbulence intensity, values of more than 1% are considered high [47]. In this case, values of about 34% are reached near the outlet deflectors, where the flow velocity is maximum. Figure 11 and Figure 12 shows the values of turbulence Reynolds number.
Figure 13 shows the pressure values inside the cabin as a function of the supply air flow rate for fixed areas of the input and output deflectors of 0.264 m2 and 0.020 m2, respectively. The speed varied in the range from 0.1 m/s to 1 m/s, and flow rate from 95 m3/h to 950.4 m3/h. The values calculated using the approximate formula turned out to be on average 40% less than the values obtained by numerically solving the hydrodynamic equations.
Figure 14 and Table 4 show the pressure values inside the cabin for a fixed supply air flow rate of 950.4 m3/h (speed 1 m/s) depending on the ratio of the areas of the input and output deflectors. In this case, the area of the input deflectors remained fixed at 0.264 m2, and the area of the output deflectors varied in the range from 0.01 m2 to 0.034 m2. The values calculated using the approximate formula also turned out to be on average 40% less than the values obtained by numerically solving the hydrodynamic equations.

4. Discussion

To estimate the pressure values from (1), the external pressures on the surface of the body and the pressure inside the cabin from different ratios of the areas of the inlet and outlet deflectors are presented below on one graph.
From Figure 15 and relation (1), we can determine the configuration of the climate system, for example, based on the speed of the train. For example, for a train to move 100 km/h, it is necessary to ensure a supply air flow rate into the cabin of at least 950 m3/h, with the ratio of the areas of the input and output deflectors having a minimum value of 22 (Table 4)—in Figure 15, these points are marked with dotted lines. In this case, the following inequality holds: 560   Pa <   P i n t < 1333   Pa .
It can be concluded that this equipment configuration can provide a maximum pressure in the cabin of 670 Pa; therefore, the fulfillment of relation (1) in this case can only be ensured up to a train speed of 120 km/h. For higher speed, it is necessary to increase either the supply air flow rate or increase the value of the ratio of the deflector areas.
Thus, it can be established that the value of the pressure boost in the cabin should be greater than the external pressure on the locomotive body, which in turn increases in proportion to the square of the speed, and for high speeds can reach significant values (Figure 8). In particular, for the locomotive under study, the pressure will increase from 120 Pa up to 1100 Pa at speeds from 50 to 150 km/h. An increase in pressure in the cabin is possible only slightly due to an increase in the supply airflow rate (increasing the fan speed) (Figure 10). In addition, an increase in the fan speed leads to an increase in the energy consumption of the air conditioner. Let us use formula (15) to determine the power of the climate system based on heat balances [32,33,34]:
Q t = q · ρ · c ρ · ∆ T ,
where q is the volumetric air flow rate, c ρ is the heat capacity of the air, ρ is the air density, and ∆T is the temperature difference at the inlet and outlet of the climate system.
From (12), we find that with an increase in flow rate from 95 m3/h to 950 m3/h (Figure 10), for example, for summer mode at ∆T = 29˚ [7,21], the cooling power increases from 2 kW to 20 kW.
The most effective way is to increase the pressure boost by reducing the area of the outlet valves, which allows us to significantly increase the pressure, and also does not require increase of the cooling or heating power of the cabin.

5. Conclusions

This paper examines the issue of assessing the required values of excess air pressure inside the locomotive cabin, which is required to prevent gas exchange between the interior of the cabin and the outside air through leaks in the cabin, including protection against the penetration of harmful substances.
In this work, a mathematical model and a numerical implementation algorithm were proposed for determining the required value of internal pressure, depending on the speed of traffic and operating modes of the climate system.
The following main results were obtained:
(a)
A constitutive relation was formulated to determine the required excess pressure inside the cabin;
(b)
To find the external air pressure, the problem of train movement in a wind tunnel was considered, the internal and external fluids domains were considered, and the values of air pressure on the cabin skin were found numerically based on the Navier–Stokes equations depending on the speed of movement. An interesting fact is the presence of zones of low relative static pressure on the outer body of the locomotive, which must be taken into account when placing inlet deflectors and setting up climate control equipment;
(c)
The values of excess internal pressure, which ensures the operation of the climate system under different operating modes, were obtained numerically based on hydrodynamic equations. The dependences of pressure value on the supply airflow rate and the area values of the input and output deflectors were studied;
(d)
To determine the approximate values of internal pressure, an applied formula was obtained, taking into account certain simplifications. The applied formula shows smaller values than the numerical results; this formula can be used for a lower estimate of the internal pressure values;
(e)
For the equipment configuration used in the work, the maximum pressure values that the climate system can provide were obtained, and the maximum locomotive speeds were indicated, based on which the system can maintain the required pressure boost;
(f)
External static pressure values (relative to atmospheric pressure) range from 5 Pa to 1129 Pa at train speeds from 10 km/h to 150 km/h;
(g)
The internal pressure values depend on the incoming air flow rate and the ratio of the areas of the inlet and outlet baffles. In particular, at an air flow of 950 m3/h (speed in inlets 1 m/s) with the ratio of the areas of the input and output deflectors, the pressure changes from 712 Pa to 59 Pa;
(h)
It was established that the amount of pressure boost in the cabin (excess pressure) must be greater than the external static pressure (relative to atmospheric) on the locomotive body, which in turn increases in proportion to the square of the speed and can reach significant values for high speeds. In particular, for the locomotive under study, the pressure will increase from 120 Pa to 1100 Pa at a speed of 50 to 150 km/h. The pressure in the cabin can only be increased slightly by increasing the supply air flow rate (increasing the fan speed). In addition, increasing the fan speed leads to an increase in the energy consumption of the air conditioner. The most effective way is to increase the pressure boost by reducing the area of the outlet valves, which allows one to significantly increase the increase in pressure, and also does not require increase of the cooling or heating power of the cabin. The work obtained the dependences of the required values of internal pressure on the areas of the output deflectors.
This research and the results obtained can be used to develop energy-efficient climate systems for locomotive cabins and other types of transport.

Author Contributions

Conceptualization, I.P. and A.N.B.; methodology, I.P. and A.N.B.; software, I.P.; validation, I.P. and A.N.B.; formal analysis, I.P.; investigation, I.P., A.N.B. and B.M.; resources, B.M.; data curation, I.P.; writing—original draft preparation, I.P. and A.N.B.; writing—review and editing, I.P. and A.N.B.; visualization, I.P.; supervision, B.M.; project administration, B.M.; funding acquisition, A.N.B. and B.M. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Acknowledgments

The authors would like to acknowledge the administration of Don State Technical University for their resources and financial support.

Conflicts of Interest

The authors declare no conflicts of interest.

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Fluids 09 00130 g001
Figure 1. External view of the locomotive for modeling external aerodynamics: (a) appearance; (b) geometric 3D model.
Figure 1. External view of the locomotive for modeling external aerodynamics: (a) appearance; (b) geometric 3D model.
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Fluids 09 00130 g002
Figure 2. Interior of the driver’s cabin for modeling internal aerodynamics: (a) interior; (b) geometric 3D model.
Figure 2. Interior of the driver’s cabin for modeling internal aerodynamics: (a) interior; (b) geometric 3D model.
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Fluids 09 00130 g003
Figure 3. Finite volume grid of a locomotive body in a wind tunnel.
Figure 3. Finite volume grid of a locomotive body in a wind tunnel.
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Fluids 09 00130 g004
Figure 4. Finite volume mesh of the cabin interior domain: (a) entrance deflectors; (b) outlet baffles.
Figure 4. Finite volume mesh of the cabin interior domain: (a) entrance deflectors; (b) outlet baffles.
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Fluids 09 00130 g005
Figure 5. External velocity field around the locomotive body for a travel speed of 110 km/h.
Figure 5. External velocity field around the locomotive body for a travel speed of 110 km/h.
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Fluids 09 00130 g006
Figure 6. Pressure field around the locomotive body for a speed of 110 km/h.
Figure 6. Pressure field around the locomotive body for a speed of 110 km/h.
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Fluids 09 00130 g007
Figure 7. Pressure field in the front part of the locomotive at a speed of 110 km/h.
Figure 7. Pressure field in the front part of the locomotive at a speed of 110 km/h.
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Fluids 09 00130 g008
Figure 8. Dependence of external pressure on locomotive speed.
Figure 8. Dependence of external pressure on locomotive speed.
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Fluids 09 00130 g009
Figure 9. Velocity and pressure streamline inside the cabin: (a) velocity streamlines; (b) pressure streamlines.
Figure 9. Velocity and pressure streamline inside the cabin: (a) velocity streamlines; (b) pressure streamlines.
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Fluids 09 00130 g010
Figure 10. Velocity vectors: (a) macro scale; (b) zoomed in.
Figure 10. Velocity vectors: (a) macro scale; (b) zoomed in.
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Fluids 09 00130 g011
Figure 11. Turbulence intensity inside the cabin: (a) view 1; (b) view 2.
Figure 11. Turbulence intensity inside the cabin: (a) view 1; (b) view 2.
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Fluids 09 00130 g012
Figure 12. Turbulence Reynolds number: (a) view 1; (b) view 2.
Figure 12. Turbulence Reynolds number: (a) view 1; (b) view 2.
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Fluids 09 00130 g013
Figure 13. Dependence of internal pressure on the supply air flow rate of the climate system: P i n   a p p l i e d —values calculated using applied formula (9), P i n   n u m e r i c a l —values calculated numerically by solving hydrodynamic equations.
Figure 13. Dependence of internal pressure on the supply air flow rate of the climate system: P i n   a p p l i e d —values calculated using applied formula (9), P i n   n u m e r i c a l —values calculated numerically by solving hydrodynamic equations.
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Fluids 09 00130 g014
Figure 14. Dependence of internal pressure on the ratio of the areas of the inlet and outlet deflectors. P i n   a p p l i e d —values calculated using applied formula (9), P i n   n u m e r i c a l —values calculated numerically by solving hydrodynamic equations.
Figure 14. Dependence of internal pressure on the ratio of the areas of the inlet and outlet deflectors. P i n   a p p l i e d —values calculated using applied formula (9), P i n   n u m e r i c a l —values calculated numerically by solving hydrodynamic equations.
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Fluids 09 00130 g015
Figure 15. Dependence of external pressure on speed and dependence of internal pressure on the ratio of deflector areas. Blue curve—dependence of pressure on train speed; red curve—dependence of pressure on the ratio of the areas of the input and output deflectors.
Figure 15. Dependence of external pressure on speed and dependence of internal pressure on the ratio of deflector areas. Blue curve—dependence of pressure on train speed; red curve—dependence of pressure on the ratio of the areas of the input and output deflectors.
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Table 1. Settings of grid models and numerical methods.
Table 1. Settings of grid models and numerical methods.
№TitleValue 1Value 2Value 3
Mesh settings for modeling external aerodynamics
1Number of cells129,203674,295985,321
2Number of nodes541,3561,253,4541,751,256
3Number of wall layers666
4Minimum cell area, m26.9 × 10−42.1 × 10−81.4 × 10−8
5Maximum cell area, m22.83 × 10−15.25 × 10−33.22 × 10−3
6Mesh orthogonality5.1 × 10−22.4 × 10−14.2 × 10−1
7Variable residual values1 × 10−41 × 10−41 × 10−4
Number of iterations for convergence of a static problem351515980
Typical pressure value, in % of the last9799.5100
Mesh settings for internal aerodynamics simulation
8Number of cells225,392489,154793,132
9Number of nodes1,016,6281,372,4081,951,499
10Number of wall layers666
11Minimum cell area, m23.1 × 10−81.2 × 10−81.1 × 10−8
12Maximum cell area, m27.5 × 10−31.43 × 10−31.22 × 10−4
13Mesh orthogonality7.7 × 10−22.2 × 10−15.6 × 10−1
14Variable residual values1 × 10−41 × 10−41 × 10−4
Number of iterations for convergence of a static problem4066141100
Typical pressure value, in % of the last9599.4100
Numerical method settings
15SolverPressure-Based
16Solution MethodsSimple
17Turbulence model k − ω
Table 2. Boundary conditions for the problem of external aerodynamics.
Table 2. Boundary conditions for the problem of external aerodynamics.
№TitleValue MinValue Max
Inlet
1Velocity, km/h0150
2PressureWe countWe count
Outlet
3Velocity, km/hWe countWe count
4Pressure00
Table 3. Boundary conditions for the problem of internal cabin aerodynamics.
Table 3. Boundary conditions for the problem of internal cabin aerodynamics.
№TitleValue MinValue Max
Inlet
1Velocity, m/s0.11
2PressureWe countWe count
Outlet
3Velocity, m/sWe countWe count
4Pressure00
Table 4. Dependence of internal pressure on the ratio of the areas of the input and output deflectors. P i n   a p p l i e d —values calculated using applied formula (9), P i n   n u m e r i c a l —values calculated by numerical solution of hydrodynamic equations.
Table 4. Dependence of internal pressure on the ratio of the areas of the input and output deflectors. P i n   a p p l i e d —values calculated using applied formula (9), P i n   n u m e r i c a l —values calculated by numerical solution of hydrodynamic equations.
№Inlet Speed, m/sConsumption, m3/h P i n   n u m e r i c a l , Pa P i n   a p p l i e d , Pa S i n S o u t S i n , m2 S o u t , m2
1195071242726.40.2640.010
2195050129622.00.2640.012
3195036021818.90.2640.014
4195027016716.50.2640.016
5195021413214.70.2640.018
6195018210713.20.2640.020
719501518812.00.2640.022
8195076478.80.2640.030
9195065428.20.2640.032
10195059377.80.2640.034
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Panfilov, I.; Beskopylny, A.N.; Meskhi, B. Improving the Energy Efficiency of Vehicles by Ensuring the Optimal Value of Excess Pressure in the Cabin Depending on the Travel Speed. Fluids 2024, 9, 130. https://doi.org/10.3390/fluids9060130

AMA Style

Panfilov I, Beskopylny AN, Meskhi B. Improving the Energy Efficiency of Vehicles by Ensuring the Optimal Value of Excess Pressure in the Cabin Depending on the Travel Speed. Fluids. 2024; 9(6):130. https://doi.org/10.3390/fluids9060130

Chicago/Turabian Style

Panfilov, Ivan, Alexey N. Beskopylny, and Besarion Meskhi. 2024. "Improving the Energy Efficiency of Vehicles by Ensuring the Optimal Value of Excess Pressure in the Cabin Depending on the Travel Speed" Fluids 9, no. 6: 130. https://doi.org/10.3390/fluids9060130

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