Development of a reduced-order virtual model of a diesel locomotive cooling module

. The article describes the process of developing a virtual model of a reduced-order cooling module for subsequent integration into a 1D virtual model of a diesel locomotive. A description of the steps in the model creation process is provided, including data collection, selection of mathematical models, and verification and validation procedures. The results of the work show that the created virtual model provides a convenient and accurate tool for analyzing and optimizing the cooling system of a diesel locomotive, which expands the possibilities for optimizing the design and improving the system control algorithms, which in turn leads to increased reliability and efficiency of its operation. The study highlights the prospects for the application of reduced-order virtual models in the railway industry.


Introduction
The modern railway industry is actively developing, striving to ensure efficient and sustainable operation of railway transport.For diesel locomotives, one of the key design considerations is the development of an efficient cooling system within the constraints of volume and power consumption.In this context, the creation of reduced-order virtual models of the cooling module of a diesel locomotive becomes an urgent task for engineers and researchers as part of the development of a unified 1D model of the operation of a diesel locomotive [1].Also, optimizing cooling processes and thermal conditions not only improves productivity and reduces component wear, but is also important from an environmental safety point of view, reducing emissions of harmful substances.
Reduced order virtual models have become a powerful tool in the field of engineering modeling and simulation, enabling efficient and accurate cooling system studies.This reduces development costs and the time before introducing new solutions into production [2].
Figure 1 shows the upper level model of the locomotive, developed in 1D application software, described in the source [3].The virtual CAE model is made in the form of a block diagram with the ability to configure using the Model-based systems engineering (MBSE) technology described in the source [4].The upper level model allows you to reproduce various operating modes of the locomotive and includes numerical models of the main systems of the product, while the relationships and mutual influence of the systems on the functioning of each other and on the entire modeling object as a whole are modeled.Each upper level model block is described by a numerical model in the form of a supercomponent (submodel, "container" for numerical models with external interfaces for communication with other blocks).The cooling system [5] is placed in a separate block "COOLING_HEATING_SYS".
The general view of the upper level model "COOLING_HEATING_SYS" block is shown in Figure 2.This block is responsible for the operation of the locomotive's cooling system and can have varying degrees of detail depending on the design stage.One of the elements of the block is a reduced-order model of the cooling module.Due to the complexity of the design and the possibility of describing the cooling module in the form of 1D elements, to assess the efficiency of the cooling process it is necessary to construct a reduced order model based on the three-dimensional design of the cooling module [6].

Development of a reduced order model of a diesel locomotive cooling module
Figure 3 shows a solid-state model of the locomotive cooling module.The main element of the cooling module is a fan located on top of the cooling module and circulating air flow through the heat exchangers with the specified parameters.In the front and rear parts inside the module, two air-to-air TONVs (charge air cooling heat exchanger) are located opposite each other, designed to cool the compressed air.In the side parts inside the module, opposite the fences in the cooling air supply openings, there are radiators that remove heat from the diesel coolant.This cooling module provides optimal conditions for reliable operation of the diesel locomotive, reducing the risk of overheating and increasing its performance in a variety of operating conditions.The initial design geometry of the locomotive cooling module was loaded in the Parasolid format so that the Y axis was directed upward and coincided with the axis of rotation of the fan, the X axis was co-directed with the direction of air supply through the inlet grilles, as shown in Figure 3. Next, using the software for preparing the calculated geometry procedures were carried out to correct geometric errors caused by the process of transferring geometry through the Parasolid format, simplifying the geometry (removing small area surfaces, closing small joints and gaps, and simplifying and removing structural parts, the influence of which on the calculation of air flow is minimal).The geometry simplification procedure is necessary in order to speed up the calculation process and increase the number of design options.
At the next step, an air domain was identified for gas-dynamic calculations, which is presented in Figure 4.In the calculated geometry of the air domain, the real fan was replaced with a virtual one with equivalent parameters (Figure 4, item 2), TONV (Figure 4, item 3) and coolant radiators (Figure 4, item 4) are replaced by geometries of porous bodies, the outlet grille is replaced by a porous body.Also, to stabilize the calculation process and speed up the process of solution convergence, the input and output areas were expanded (Figure 4, pos. 1 and 5).Table 1 shows the thermophysical parameters of air [7,8], which were used in the project for numerical simulation of the flow through the cooling module of a diesel locomotive.The dependence of thermophysical parameters is interpolated by polynomial dependences on temperature.
Table 1.Thermophysical parameters of air.

Parameter
Value Density, kg/m 3  Ideal gas Specific heat capacity, J/(kg K) 1028.5-0.20865ꞏT+0.00047945ꞏT 2 -3.1342e-08ꞏT 3 -1.2392e-10ꞏT 4   Thermal conductivity, W/(m K) 0.0026846+7.820100000000001e-05ꞏT-1.153e-08ꞏT 2 +1.0588e-22ꞏT 3 Viscosity, kg/(m s) 4.2334e-06+4.9802e-08ꞏT-8.649e-12ꞏT 2 Molecular weight, kg/kmol 28.84 It was mentined above that charge air cooling units (Figure 4, item 3) and coolant radiators (Figure 4, item 4) are replaced by geometries of porous bodies.These model elements have a complex cellular structure, the resolution of which by a computational grid is impractical.Also, the geometry of the output grille after the fan and the cooling fins of the electric motor was replaced with a porous body, because they have a periodic structure with a clear direction of air flow.Porous bodies have anisotropic properties.Figure 5 shows geometry elements that are replaced by equivalent porous bodies: liquid cooling radiators (Figure 5, item 1), TONV (Figure 5, item 2), electric motor cooling fins (Figure 5, item 3), output grille (Figure 5, item 4).For a model of an anisotropic porous body, you need to set: − vector components for two directions of the porous medium (for the third direction the components are determined automatically).
− coefficients for the model of viscous resistance (resistance is proportional to the speed of the flowing medium) and inertial drag (resistance is proportional to the square of the speed of the flowing medium); − porosity of the medium.
In the used formulation of the Absolute Velocity Resistance Formulation model of porous bodies, the porosity of the medium can be taken equal to the default value, because does not affect the result.
The vector components in directions 1 and 2 for models of porous bodies are determined from the geometry of the model (Figure 4 and 5) and are shown in Table 2.The inertial resistance coefficients for the porous media of the engine cooling fins and the output grille are determined from the reference book of hydraulic resistances for the grilles (in direction 1) and for the channels (in direction 2).The viscous resistance coefficients for these elements are taken equal to 0, the resistance in the direction perpendicular to the planes of the ribs (in direction 3) is several orders of magnitude greater than in directions 1 and 2, which ensures the absence of flow in this direction and ensures the stability of the solution compared to shutdown calculation of flow equations in this direction.The coefficient values are given in Table 3.To simulate the air flow through the fan of the locomotive cooling module, the 3D Fan Zone engineering model is used.Using the 3D Fan Zone model allows you to replace the "real" fan design with a disk with equivalent characteristics.During the calculation process, the results of the integral characteristics are comparable to the results of direct modeling with moving coordinate systems.At the same time, the cost of machine resources is significantly less, and this allows you to speed up the process of calculating many design points.The 3D Fan Zone model does not require calculating the rotation of the mesh; it is possible to set the width of the fan in the direction of the flow, as well as determine the tangential and radial components of the speed.
3D Fan Zones are a zone of fluid cells that simulate the effect of an axial fan by applying a distributed pulse source to a disk-shaped volume of fluid (i.e., the volume covered by the blades).The parameters of the equivalent disk are selected based on the cross-section of the volume swept by the fan blades.The cross-sectional area of the volume formed by the rotation of the fan blades of a real design is equal to 0.036199 m2 (Figure 6,a).The outer radius of the fan is 0.805 m, the inner radius is 0.28 m.The cross-sectional shape of the virtual fan disk is a rectangle.Based on the parameters of the cross-section of the fan torus, the height of the disk should be equal to 0.06895 m (Figure 6,b).Table 4 shows the parameters of the 3D Fan Zone virtual disk.Figure 7 shows the flow-pressure characteristics of the fan.The parameters of the fan flow-pressure characteristics for the 3D Fan Zone were selected from a comparative analysis of numerical and physical experiments.Additionally, points have been added to ensure smooth interpolation of the flow-pressure characteristic by a second-order polynomial, which will be used to extrapolate data when carrying out calculations.The computational mesh used for this problem is polyhedral.Polyhedral cells allow you to construct a mesh that provides high calculation accuracy and is economical in terms of computational resources.Also, the use of polyhedral cells makes it possible to carry out calculations for highly turbulent flows.To evaluate and more accurately calculate the flow around the straightening vane blades, mesh refinement was specified.The minimum cell size was set to 1 mm, the maximum size was 60 mm, the degree of curvature was 12.The parameters of the prismatic layer were specified as follows: the height of the first layer was 500 μm, the number of layers was 3, and the growth coefficient was 1.2.
The final computational grid for numerical modeling of air flow in the cooling module of a diesel locomotive is presented in Figure 8.The total number of cells on average for all computational geometries was approximately 5,944,547, the number of nodes was 22,504,101.In accordance with the initial data, a plan of computational experiments was prepared to build a ROM model of the locomotive cooling module, which is presented in Table 5.To develop a numerical modeling project, the following boundary conditions were set, which are shown in Figure 9.At the inlet (Figure 9, item 1) and exit (Figure 9, item 2) the pressure is set to the computational domain.Inlet pressure and temperature are transmitted as a parameter and are used to form the ROM model.The inlet and outlet pressures are set to 99,324 Pa, which corresponds to ambient air pressure.The outlet air temperature is equal to the inlet air temperature, because the cooling module uses ambient air to operate.Additionally, to determine the parameters of the air in front of the heat sink and radiators, as well as the connection of the virtual disk of the 3D Fan Zone fan, internal surfaces and interfaces were determined.

Results of constructing a reduced order model of the locomotive cooling module
To build a ROM model in a project for three-dimensional numerical modeling of air flow in a diesel locomotive cooling module in ANSYS Fluent, 7 input and 20 output parameters were determined, which are shown in Table 6.Named Expressions were used to determine input parameters, and reports were used for output parameters Report Definition. Figure 10 shows the project diagram in the ANSYS Workbench environment.The basic block for building a ROM model is a project for three-dimensional modeling of air flow through the cooling module of a diesel locomotive.All project parameters are determined automatically.To build a ROM model, you need to add a response surface construction block to the parameterized project.The standard Central Composite Design search method was selected to obtain the response surface, and the study type was determined automatically.The ranges for the values of the input parameters are set according to Table 5.After determining the limits for changing the parameters and choosing a research method in the ANSYS Workbench environment, a plan of computational experiments is generated.As a result of a series of calculations based on the given boundary values of the input parameters, a multi-parameter response surface is created.It is enough to export this surface as a file directly into a 1D diagram of the operation of the locomotive cooling system.
Figure 11 shows the degree of influence of the input parameters on the value of the target functions.As can be seen from the figure, the fan speed has the greatest influence.As the rotation speed increases, the efficiency of the cooling module increases.Thus, one of the main tools for regulating cooling will be adjusting the rotation speed.Environmental conditions have less influence.

Conclusion
The possibility of creating a ROM model of a reduced order of the cooling module of a diesel locomotive for subsequent integration into the general 1D diagram of the operation of a diesel locomotive is shown.
The use of engineering fan models and porous and simplified geometries in the reduced order model reduces the number of elements and simplifies calculations, which allows you to use less computing resources and perform calculations in a short time.
Creating a reduced-order model is a trade-off between accuracy and computational performance.Depending on the specific requirements and constraints of the project, the level of reduction may vary.In general, the ROM model of the diesel locomotive cooling module allows for more efficient analysis and optimization of the cooling system, which leads to a more efficient and economical use of computing and time resources.

Fig. 2 .
Fig. 2. Structure of the model of the cooling and heating system of diesel locomotive engines.

Fig. 6 .
Fig. 6.The cross-sectional area of the fan torus and the virtual disk: a) the cross-sectional shape formed by the rotation of the fan blades of a real design; b) cross-sectional shape formed by the rotation of the virtual fan blades.

Fig. 8 .
Fig. 8. Calculation grid for numerical simulation of air flow in the cooling module of a diesel locomotive.

Table 5 .
Plan of computational experiments for preparing a ROM model of a diesel locomotive cooling module.

Fig. 9 .
Fig. 9. Boundary conditions for numerical simulation of air flow inside the cooling module of a diesel locomotive.

Fig. 10 .
Fig. 10.Calculation scheme for constructing a ROM model of a reduced order of a diesel locomotive cooling module.

Fig. 11 .
Fig. 11.Diagram of the degree of influence of input parameters on the values of target functions.

Table 2 .
Coefficients of direction vectors of porous zones.

Table 3 .
Resistance coefficients of porous zones.

Table 6 .
Project parameters for 3D numerical simulation of air flow in a diesel locomotive cooling module in ANSYS Fluent.