Analysis of the Sum Minimization Possibilities of Heat Exchanger Core Masses in Internal Combustion Engine Cooling Systems

Abstract

Rational designs for cooling systems (CS) of internal combustion engines are formulated in the form of a series of circulation circuits. The engine is integrated into a circuit with the highest and unregulated flow of internal circuit coolant (ICC). All heat exchangers are placed in circulation circuits with relatively reduced and adjustable ICC flow rates. While the circuits are usually interconnected, they can also be designed to operate independently. This CS scheme enables the achievement of the minimum possible value of the sum of masses of exchanger cores, denoted as M_Σ. The reduction in M_Σ is achieved through the regulation of ICC flow in a closed circulation loop involving two heat exchangers. The variations in M_Σ based on the circuit parameters have been thoroughly investigated. The reduction in M_Σ can also be applicable to more intricate systems. A decrease in M_Σ, under identical initial CS parameters, may occur in different magnitudes, depending on the specific features of the CS scheme and the operating conditions of the heat exchangers within it. Cooling systems, constructed with the same initial parameters and comprising multiple circulation circuits that meet all criteria for rational design, may exhibit diverse configurations. Examples of such systems are explored, and the minimum values of M_Σ are calculated for each. It has been determined that the disparity in the minimum values of M_Σ for such systems, while maintaining equal efficiency, can exceed 30%. The selection of the optimal CS scheme is contingent not only on achieving the minimum possible value of M_Σ but also on various other factors.

1. Introduction

The motivation for this work is to demonstrate the potential reduction in M_Σ in different cooling system schemes by regulating ICC flow rates in circulation circuits. To achieve this objective, ICC flow rates can be regulated in both simple and more complex cooling system configurations. However, variations exist in achieving the minimum M_Σ for different cooling system schemes, necessitating an exploration of the features influencing M_Σ reduction in various schemes and the reasons for these differences. Modern cooling systems for internal combustion engines are currently implemented through various circulation circuits [1]. The reduction in the total mass of the cores is achieved by leveraging the effect of regulating the flow rate of the ICC in a closed circuit of two heat exchangers [2]. It is noteworthy that, in all works known to us, the focus is on the maximum reduction in the temperature of the coolant downstream of the cooler rather than a decrease in the total mass of the heat exchanger cores, denoted as M_Σ [3].

The foundational aspects of the problem are discussed in [4,5], where the focus is on maximizing the reduction of the cooled coolant temperature. The problem is addressed using numerical methods in the context of the simplest circulation circuit. Works such as [6,7,8,9] delve into the design possibilities of cooling systems in the form of circulation circuits. While acknowledging the potential for rationalizing cooling systems by regulating ICC flow through heat exchangers, these works lack clear recommendations on the choice of ICC expenditures. Similar observations apply to [10,11,12,13].

In [14], the regulation of ICC consumption through the branches of a rational cooling system scheme is explored to reduce M_Σ. However, the article does not analyze the possibilities and consequences of reducing M_Σ in various specially designed systems with such regulation. In article [15], the authors optimize the cooling system of a marine diesel engine by regulating pump performance while keeping the system design unchanged but open to improvement. Article [16] addresses the enhancement of a cooling system by regulating ICC consumption based on the main engine mode, suggesting the replacement of traditional mechanically driven pumps with electrically driven pumps.

Fundamentally different cooling systems are also under consideration. A comprehensive review of modern adsorption refrigeration systems is provided in [17,18]. However, these systems are characterized by significant dimensions, making their practical use challenging. A substantial portion of the work is dedicated to examining the impact of cooling system operation on engine parameters. Inadequate cooling conditions can result in engine overheating, incomplete combustion, and poor environmental and economic performance [19,20]. Ineffectual cooling also amplifies the cost of consumables [21,22]. In general, phenomena associated with improper cooling conditions contribute to an increase in the concentration of harmful substances in exhaust gases, particularly NOx emissions, power loss, and excessive wear, ultimately leading to a reduction in service life [23,24]. Reducing the service life of machines is detrimental to the environment.

Therefore, any effort aimed at enhancing engine efficiency through effective cooling is crucial, as it results in a reduction in COx emissions [25,26]. Many studies have explored the potential of modifying cooling systems to decrease engine exhaust emissions [27,28,29]. Additionally, numerous numerical analyses have been conducted to optimize heat distribution in engines, with the goal of minimizing pollutant emissions and reducing fuel consumption [30,31,32].

Part of this field of study is dedicated to the selection of ICC type. In this article, the authors focus on considering fresh water as an ICC, a choice that facilitates the comparison of cooling systems under equal conditions. However, there is potential for further enhancing cooling system parameters through the use of Nan fluids [33,34,35]. Notably, [36] suggests that cooling system parameters experience significant improvement when utilizing liquids containing graphene oxide, created based on a combination of ethylene glycol and water. Additionally, [37], a study by Hossen and Sakib, involves numerical simulations of a cooling system, demonstrating that the use of Nan fluids with various compositions notably enhances heat transfer conditions in the cooling system.

For a closed circulation loop consisting of two heat exchangers and two pumps (the simplest cooling system scheme), there are significant variations in M_Σ when using optimal and non-optimal ICC flow rates. Similar substantial differences in the values of M_Σ are observed in more complex cooling systems, even under identical external conditions, system efficiency, and engine parameters. These disparities are inherent, and it is imperative to identify and elucidate their underlying causes.

The reduction in M_Σ stands out as one of the primary key parameters that determine the competitiveness of a cooling system. In principle, the potential for reducing M_Σ is evident when the charge air cooling temperature is fixed. However, the task of minimizing M_Σ has not yet been explicitly defined or considered as a primary objective, despite its significance. This aspect merits further exploration and attention in the context of cooling system design.

2. Materials and Methods

To analytically address the problem, it is essential to examine a closed system of equations that characterizes the movement of coolant flows and heat flows within the cooling system. However, solving this closed system of equations for the desired quantity (in this case, M_Σ), even for the simplest cooling system scheme, results in complex and non-differentiable expressions. Therefore, numerical calculations become necessary. The authors conducted calculations for both the simplest cooling systems with various parameters and more complex systems characteristic of modern internal combustion engines. In the direct calculations of the cooling system, the following parameters were established and determined.

The following were determined: the efficiency of all heat exchangers of the system; the flow rates of coolants through all heat exchangers; all unknown temperatures of coolants; and the masses of the heat exchange elements (cores) of every heat exchanger and of all exchangers of the system, M_i and M_Σ.

The following parameters were specified: sea water inlet temperature (T_ww1), air temperature behind the compressor (T₁), temperatures of water and oil behind the engine (T_wm2, T_om2), air temperature in the engine receiver (T_s), fresh water flow through the engine (G_wm, equivalent to the flow through the fresh water pump), sea water flow through the pump (G_ww), oil flow through the pump (G_m), and charge air flow (G_c). The system was designed to remove strictly defined heat flow values into water, oil, and hydraulic fluid (specified as Q_e, Q_m, and Q_h, respectively). The main (stereotypical) parameters of the designs of all heat exchangers and the efficiency level in utilizing the masses of their cores (represented by coefficients k_gi) were also established.

To expedite the design process and ensure the requisite accuracy, all elements of the system design need to be integrated into a unified mathematical model, often referred to as a calculation complex. This complex should incorporate both direct and feedback connections between interacting elements.

When calculating systems, the following assumptions were made:

• The heat transfer process in the design mode is steady.
• Heat losses in the sections of pipelines connecting the heat exchangers are insignificant.
• The ambient temperature is the same for all elements of the cooling system.
• The oil used in the engine system has properties that are practically no different from those specified in the standard for grade M-14W2 (interstate standard 12337-84) [38].

System calculations were performed taking into account the conditions of unambiguity.

The basis for direct thermal calculation of the circuit is a system of equations consisting of:

• Heat balance equations for all heat exchangers and the entire cooling system;
• Equations of heat flows in the system;
• Heat balance equations at mixing points of coolant flows;
• Mass balance equations at mixing points of coolant flows;
• Efficiency equations for all heat exchangers;
• Relationship equations between the efficiency of all heat exchangers and their NTU;
• Expressions of the relationship between NTU and the masses of the cores of all heat exchangers.

When working with a specific system of equations, a unique solution can be obtained if the number of equations is equal to the number of unknowns.

For example, in the scheme presented in Figure 1, it is necessary to determine the values of 21 unknowns based on the original system of 19 equations.

Obviously, to achieve an unambiguous solution, it is necessary to additionally specify the values of two unknowns, and the remaining unknowns can then be calculated based on the system of equations. Any two unknowns can be chosen to be set, and it is logical to designate the values of ICC flow rates through the oil cooler and charge air cooler. Moreover, the real regulation of the cooling system will be carried out precisely by adjusting these flow rates. However, the mathematical solution of the problem in this case will be challenging. It is most convenient to assign temperature values to the ICC behind the oil cooler and charge air cooler, denoted as t_wo2 and t_wc2. This approach simplifies the problem’s solution considerably. The quantities t_wo2 and t_wc2 are uniquely related to the ICC flow rates through these heat exchangers; accordingly, optimizing the system becomes more convenient by setting various possible values for these temperatures. As a result, the curves M_Σ = f (t_wo2) and M_Σ = f (t_wc2) were obtained. To regulate ICC, it is not difficult to obtain similar dependences on ICC flow rates.

For the calculated cooling systems, each curve was plotted at a constant (and rational) value of other specified temperatures. During the initial construction of curves, rational (and constant) values of other temperatures (except for the one changed to construct the curve) were approximated, and then refined based on previously constructed ones. The ultimate value of the minimum parameter, M_Σ, was achieved with the same (within the possible error) value of this parameter for all curves. Essentially, this approach outlines one of the methods to obtain an extremum using the coordinate descent method.

3. Results and Discussion

The first system to be studied was the simplest cooling system, as depicted in Figure 2.

A similar scheme was previously studied for a slightly different purpose in [4,5]. In this context, dependencies are derived for such a scheme to observe how M_Σ changes when regulating the consumption of ICC (Figure 3).

When constructing graphs and conducting further analysis, the parameter η₀ is utilized, representing the efficiency of the cooling system for cooling the charge air

$${\eta }_0=\frac{T_1-T_s}{T_1-T_{ww1}},$$

where T_1,s—temperatures of charge air in front of the compressor and in the engine receiver, K; T_ww1—temperature of external circuit coolant (ECC) in front of the cooler, K.

The dependencies were plotted for various values of η₀ and different external circuit coolant costs—G_ww. The calculations were conducted for one of the modern medium-speed marine engines, and the necessary parameters for these calculations are provided in

Table 1. The main parameters of the engine for which the simplest cooling systems were calculated.

Designation	Items	Values
Ne	Engine output (kW)	1000
n	Engine speed (rpm)	500
pc	Boost pressure (bar)	2.0
Gc	Charge air flow (kg s−1)	0.9
p0	Ambient pressure (bar)	1.0
t0	Ambient temperature (°C)	40.0
t1	Air temperature after compressor (°C)	181.35
tww1	Sea water temperature in front of the pump (°C)	30.0
t2	Air temperature in the receiver (°C)	35.0

.

In greater detail, the initial section of one of the curves in Figure 3 is illustrated in Figure 4. Here, it can be observed that it exhibits a characteristic bend, influencing the value of M_Σ at low ICC flow rates.

Analysis of the dependencies in Figure 3 and Figure 4 allows us to note the following features.

• In a closed simple circuit, there is a significant variation in M_Σ depending on the flow of ICC through the heat exchangers.
• As G_w increases from values close to zero, the value of M_Σ first decreases (Figure 4), and then consistently increases monotonically for any constant values of η₀.
• For all possible η₀, the minimum values of M_Σ are achieved at relatively low values of the ICC flow rate G_w.
• The values of M_Σ decrease as G_w decreases and increase as G_w increases.
• The increase in M_Σ depending on G_w varies for different values of η₀; as η₀ as η0 increases, the growth of M_Σ becomes more pronounced.
• The ratios M_Σ for two different η₀ increase as the values of η₀ and the absolute value of M_Σ rise—they can exceed 1000% in the region of large values of G_w within practical ranges of G_w and η₀.

Next, an analysis was conducted on the position of the minimum points of M_Σ for the simplest cooling system, depending on the ratio of the energy capacities of the coolants in the charge air cooler S_c.

S_c = W/W_w,

where W = G_H·c_pH; W_w = G_w·c_pw—the energy capacities being referred to are those of the charge air and internal circuit coolant, respectively; c_pH—the isobaric heat capacity of air; c_pw—the heat capacity of internal circuit coolant.

The position of the minimum point M_Σ for various values of η₀ and G_ww was determined by analyzing the initial sections of the curves M_Σ = f (S_c). Examples of such regions are shown in Figure 5 and Figure 6.

The position of the minimum points allows for some deviations associated with the shape of the curves and the specifics of the systems and heat exchangers under consideration. Based on the comprehensive analysis, it is evident that the value of S_c, corresponding to the minimum value of M_Σ, practically depends only on η₀ and can be reasonably approximated by the expression

S_c = 6.0263η₀ − 5.0311.

It has also been established that for the range η₀ = 0.90…0.95 with rational S_c (corresponding to the minimum value of M_Σ), the charge air cooler efficiency value is approximately constant and corresponds to t₀

η_c ≈ 0.97.

With an irrational value of S_c, the efficiency of the charge air cooler, η_c, significantly affects M_Σ. The value of M_Σ decreases monotonically with increasing η_c. If in the simplest cooling system, the flow rate of ICC, G_w, is increased to the possible limit (up to the consumption through the engine), then the value of M_Σ will increase. The value of M_c can either increase or decrease.

For example, for an engine whose parameters correspond to Table 1, at η₀ = 0.9 and G_w = 4.0 kg s⁻¹ (optimal S_c), the value of M_Σ = 281.5 kg, M_c = 126 kg at η_c = 0.97.

At η₀ = 0.9, G_w = 22.2 kg s⁻¹ (maximum G_w), then M_Σ = 416.9 kg, M_c = 136.2 kg, η_c = 0.99.

At η₀ = 0.953 (for optimal S_c), the value is M_Σ = 394 kg, M_c = 211 kg (optimum G_w = 2.0 kg s⁻¹, η_c = 0.97).

At η₀ = 0.953, G_w = 22.2 kg s⁻¹ (maximum G_w), the value is M_Σ = 1201 kg, M_c = 135 kg (η_c = 0.99).

As can be seen from the provided data, the variation in M_Σ is contingent on η₀ and exhibits a substantial increase with its growth, aligning with one of the conclusions drawn.

The efficiency of the second heat exchanger, η_w, contingent on η₀, and for the same range of η₀, can be approximated by the expression

η_w = 0.2941η₀ + 0.667.

The accuracy of cooling system calculations and potential errors primarily depend on the precision of heat exchanger calculations. This work employs widely accepted methods for calculating heat exchangers, and system calculations are carried out based on established mathematical and thermal engineering principles. The objectives of this work preclude the possibility of experimental verification for all the presented material. Nevertheless, the key results of experimental checks related to the accuracy of heat exchanger calculations and the validity of calculation methods for the cooling system can be provided. These checks were conducted to validate the calculations of the simplest cooling system, serving as the foundation for all subsequent calculations. Specifically, the elements of boundary conditions for heat exchangers were scrutinized, and the correctness of the chosen methods for cooling system calculations was verified. The primary outcomes are presented in

Table 2. Estimation of errors for charge air cooler.

Designation	Items	Values			Note
		I	II	III
t2	Air temperature after charge air cooler (°C)	35.81	35.71	34.41	Calculation
		35.70	35.52	34.12	Experiment
∆t2	Difference air temperature after charge air cooler (°C)	0.11	0.19	0.29
Δp	Air resistance (bar)	0.0157	0.0107	0.0095	Calculation
		0.0150	0.0101	0.0090	Experiment
δ	Difference air resistance	0.045	0.058	0.049
ηc	Charge air cooler efficiency	0.94	0.95	0.97
Gc	Charge air flow (kg s−1)	0.9	0.7	0.6	Experiment
p1	Boost pressure (bar)	2.0	1.7	1.5	Experiment

,

Table 3. Estimation of errors for central cooler.

Designation	Items	Calculation	Experiment
Gw	ICC flow rate by fresh water pump (kg s−1)	0.32
Gww	ECC flow rate by sea water pump (kg s−1)	5.50
tw1	Inlet ICC water temperature (°C)	91.46	91.40
tw2	Outlet ICC water temperature (°C)	30.02	30.30
tww1	Temperature of ECC in front of the cooler (°C)	30.00	30.00
Δpw	Resistance by ICC (bar)	0.00268	0.00305
Δpww	Resistance by ECC (bar)	0.00137	0.00123
δw	Error Δpw	0.139
δww	Error Δpww	0.105
ηw	Central cooler efficiency	0.999	0.995

and

Table 4. Estimation of errors for cooling system.

Designation	Items	Calculation	Experiment	Measurement Error
tww1	Temperature of ECC in front of the cooler (°C)	30.00	30.00	± 0.30
t1	Air temperature after compressor (°C)	125.78	126.20	± 0.70
t2	Air temperature after charge air cooler (°C)	35.00	37.20	± 0.75
tw1	Charge air cooler inlet water temperature (°C)	30.22	31.30	± 0.30
tw2	Charge air cooler outlet water temperature (°C)	91.46	91.40	± 0.75
p0	Ambient pressure (bar)	1.0	1.013	δp = 0.028
p1	Boost pressure (bar)	2.0	1.956
Gc	Charge air flow (kg s−1)	0.9	0.9 *	δG = 0.020…0.025
Gww	ECC flow rate by sea water pump (kg s−1)	5.5	5.5 *
Gw	ICC flow rate by fresh water pump (kg s−1)	0.32	0.32 *
ηc	Charge air cooler efficiency	0.950	0.934	δ ** = 0.030…0.037
ηw	Central cooler efficiency	0.996	0.994
η0	Cooling system efficiency	0.950	0.954

* Measured with specified error. ** For the entire measurement range.

.

Checks were conducted for different objects under various conditions, reflecting the diverse characteristics of both the objects and the feasibility of experimental verification for fairly large full-scale objects. The results from the tables indicate that the checks yielded quite satisfactory outcomes, providing a solid basis to consider all the information presented here as reliable.

The patterns identified for the simplest circuit can be extrapolated to more complex cooling system circuits if they incorporate the simplest circuit without modifications. However, there exist numerous cooling system schemes that utilize the concept of regulating the flow of ICC through heat exchangers, yet cool the coolants under conditions that do not align with those discussed above.

Below, we explore more complex systems in which the charge air cooler is integrated into the overall circuit, and another where it operates in a separate circuit. These systems are designed for an engine with parameters outlined in

Table 5. The results of the system calculations for various loads and ambient temperatures.

Designation	Items	Values
Ne	Engine output (kW)	2950
N	Engine speed (rpm)	1000
pc	Boost pressure (bar)	2.94
Gc	Charge air flow (kg s−1)	5.30
p0	Ambient pressure (bar)	1.0
t0	Ambient temperature (°C)	40.0
t1	Air temperature before compressor (°C)	181.35
tww1	Sea water temperature in front of the pump (°C)	30.0
t2	Air temperature in the receiver (°C)	48.0
tm1	Engine oil temperature behind the engine (°C)	90.0
th1	Hydraulic fluid temperature behind the system (°C)	90.0
Gw	ICC flow rate by fresh water pump (kg s−1)	22.2
Gww	ECC flow rate by sea water pump (kg s−1)	22.2
Gm	Oil flow rate (kg s−1)	26.6
Gh	Hydraulic fluid flow rate (kg s−1)	4.0
Qe	Heat flow from engine cylinders (kW)	1058.0
Qm	Heat flow from oil (kW)	531.4
Qh	Heat flow from hydraulics (kW)	40.0

. Both circuits and their heat exchangers are state-of-the-art. The selected schemes are evaluated at η₀ = 0.9.

Since the definition of M_Σ is linked to specific designs of heat exchangers and types of heat exchange surfaces, the numerical values of the masses of the heat exchanger cores cannot be considered absolute, even for engines with similar parameters. However, the obtained mass values are convenient for comparing different options.

The first of the cooling systems with a complex circuit is the type A cooling system (Figure 1). For this system, the highest value of the minimum M_Σ was obtained. The circuit is designed with a charge air cooling circuit integrated into the overall system circuit.

The hot ICC is discharged from the full-flow circuit of the cooling system after the engine has cooled. ICC from the full-flow circuit enters the cooler for cooling, after which it bifurcates into parallel flows to cool the charge air in the charge air cooler and the oil in the oil cooler. Subsequently, the ICC streams are combined, and the merged stream, with a temperature T_wb and flow rate G_wb, enters the full-flow cooling system loop before the fresh water pump. When combining the ICC flows after the engine and after the heat exchangers, the ICC temperature decreases to the required value T_mw1 in front of the engine. The results of minimizing M_Σ are presented in

Table 6. Main parameters of the cooling systems at the minimum M_Σ.

Designation	Items	Cooling System Type
		A	B	C	D	E
		Values
ηh	Charge air cooler efficiency	0.995	0.993	0.968	0.967	0.944
Sh	Energy-capacity ratio	0.225	0.30	0.389	0.374	0.403
Mh	Charge air cooler core mass	178.3	194.9	137.7	157.6	115.7
Ixh	Dimensionless criterion for charge air cooler	1504	1.498	–	–	–
ηw	Central cooler efficiency	0.808	0.735	–	–	–
Sw	Energy-capacity ratio	0.62	0.663	–	–	–
Mw	Central cooler core mass	1011.4	756.0	–	–	–
Ixw	Dimensionless criterion for central cooler	1.947	1.476	–	–	–
ηwc1	Central cooler No. 1 efficiency	–	–	0.864	0.867	0.907
Swc1	Energy-capacity ratio	–	–	0.153	0.159	0.119
Mwc1	Central cooler No. 1 core mass	–	–	153.4	165.6	151.2
ηwc2	Central cooler No. 2 efficiency	–	–	0.851	0.965	0.806
Swc2	Energy-capacity ratio	–	–	0.329	0.193	0.147
Mwc2	Central cooler No. 2 core mass	–	–	378.5	347.8	353.7
ηwc3	Central cooler No. 3 efficiency	–	–	–	0.547	–
Swc3	Energy-capacity ratio	–	–	–	0.139	–
Mwc3	Central cooler No. 3 core mass	–	–	–	48.2	–
ηg	Hydraulic fluid cooler efficiency	–	–	0.555	0.717	0.43
Sg	Energy-capacity ratio	–	–	0.268	0.157	0.549
Mg	Hydraulic fluid cooler core mass	–	–	38.9	39.2	25.7
ηoc	Oil cooler efficiency	0.365	0.565	0.555	0.717	0.486
Soc	Energy-capacity ratio	0.624	0.399	0.536	0.314	0.549
Moc	Oil cooler core mass	251.7	312.7	454.7	392.0	362.5
Ixoc	Dimensionless criterion for oil cooler	0.52	0.617	–	–	–
MΣ	Total mass of cores heat exchangers	1441.4	1263.6	1163.2	1150.4	1008.8
Ixcs	Dimensionless criterion for cooling system	3.972	3.591	–	–	–

. The operational efficiency of each heat exchanger in the cooling system is characterized by the dimensionless criterion I_x [39].

$$I_{\mathrm{x}}=\frac{Q_i}{\Delta T_i{W}_{i\mathrm{x}}},$$

where Q_i—the heat flow through the heat exchanger, W; ΔT_i—temperature difference between heat carriers (average logarithmic temperature difference), K; W_ix—energy intensity of the cold coolant, W/K.

When comparing a number of systems, it is necessary to consider their differences and account for changes within the systems. Simultaneously, this applies to both heat exchangers and the overall system

$$I_{\mathrm{x}\mathrm{c}i}=I_{\mathrm{x}pi}\frac{W_{\mathrm{x}\mathrm{c}\mathrm{c}}}{W_{\mathrm{x}\mathrm{e}\mathrm{c}}}$$

where I_xci—adjusted criterion; I_xpi—the initial value of the criterion; W_xcc—the energy capacity of the cold coolant for the compared system, W/K; W_xec—the energy intensity of the cold coolant for the reference system, W/K.

As M_Σ increases in the system, the I_x criterion also increases, and vice versa. Therefore, when designing both systems and heat exchangers, one should aim to minimize the numerical value of the criterion. In this case, all systems will be compared with cooling system type A, considering it as the least favorable among those compared. Type A cooling system is regarded as a reference.

Next, a type B cooling system was studied (Figure 7). In this system, the hot ICC flow is extracted from the full-flow circuit for cooling after the fresh water pump (FWP1), before reaching the engine. The ICC then enters the inlet of the second fresh water pump (FWP2), after which it flows into the central cooler, where it is cooled to temperature t_w1.

Then, it flows to the inlets of the charge air cooler and oil cooler, and after passing through these coolers, the ICC returns to the full-flow circuit. After the coolers, the ICC flows are combined and, at a temperature t_wt, they proceed to the inlet of the FWP2 pump. By incorporating a portion of the cooled ICC flow into the full-flow circuit, at the input of FWP1, and mixing it with the flow leaving the engine, the temperature t_mw1 is maintained in front of the engine. The key parameters of this cooling system and other schemes, at the minimum of M_Σ, are presented in Table 6.

As evident from Table 6, for the type B cooling system, the minimum value of M_Σ is significantly reduced compared to the previous version. In alignment with the I_xw criterion value, the heat exchanger with the largest core mass in this system operates under conditions of a higher temperature difference than the previous scheme. The masses of the charge and oil cooler cores experienced slight increases, but a substantial reduction in M_Σ was achieved, as confirmed by the corresponding criterion. In principle, for any cooling system, an increase in the sum of the masses of the heat source cores is accompanied by a decrease in the sum of the masses of the heat sink cores and vice versa. The patterns of growth and reduction in the masses of heat exchanger cores depend on the adopted design of the cooling system.

Comparing the first two cooling systems, the following observations can be made. In the cooling system type A circuit, hotter fuel oil is extracted from the full-flow circuit than in the cooling system type B, but this does not result in an increase in the temperature difference on the central cooler. At first glance, the indicated temperature difference should have increased, but this did not happen. The organization of the previous system imposes certain restrictions on reducing the costs of ICC through heat exchangers. Specifically, it is impossible to achieve the required ICC temperature in front of the engine if its flow through these heat exchangers is too low. This, in turn, limits the increase in temperature difference for the central cooler.

As shown in Table 6, η_c exceeds the value corresponding to the minimum M_Σ for the simplest circuit. The value of S_c is very close, and the core mass is greater. This is attributed to the rationalization of other heat exchangers in the circuit. It should be noted that the values of S for the oil cooler and central cooler for the schemes under consideration significantly exceed the values that occur for circuits that do not take advantage of the effect of reducing ICC consumption. As per Table 6, M_Σ for the type B system decreased by almost 180 kg compared to the type A system. The primary reduction was achieved by reducing the mass of the central cooler core.

Let us examine a type C cooling system scheme (Figure 8), in which a reduction in M_Σ is achieved by increasing the number of central coolers. This offers expanded possibilities for regulating the flow of ICC through heat exchangers (Table 6).

This and the subsequent systems utilize a hydraulic fluid cooler. The mass of its core is very small, approximately 39 kg. For this reason, the presence of this heat exchanger has no practical impact on the comparison results of the cooling systems. The values of η_c, S_c, and M_c here are close to the values established for the simplest circuit. The parameters of the remaining heat exchangers are determined based on the decrease in M_Σ. The reduction in M_Σ for this system, compared to the previous one, is more than 100 kg. Compared to cooling system type A, it is about 280 kg. A further reduction in M_Σ can be achieved through even better possibilities for regulating ICC flow rates through the system heat exchangers. However, for the considered schemes and similar ones, these possibilities are practically exhausted. Increasing or even maintaining the temperature difference for the heaviest heat exchangers is challenging. This can be illustrated by the diagram of the type D cooling system (Figure 9). A central cooler No. 3 is installed here, which should remove part of the heat flow from the engine and expand the possibilities of regulating the flow through other heat exchangers. However, due to the installation of this cooler, the temperature differences in all heat exchangers are reduced, except for the central cooler No. 3, which counteracts a further significant decrease in M_Σ (Table 6).

As an alternative cooling system scheme, which also implements the idea of reducing M_Σ by regulating the flow of ICC through each heat exchanger, and where the operation of the heaviest heat exchanger is ensured under conditions of increased coolant temperature difference, a type E scheme is presented (Figure 10).

The main results of the calculation of the system when the minimum M_Σ is reached are presented in Table 2.

The results of the calculation of the system when the minimum M_Σ is reached are also presented in Table 6. As observed, the main parameters of the heat exchangers change little, but they all contribute to a decrease in M_Σ. Consequently, M_Σ is significantly reduced (almost 142 kg compared to the previous system). However, another fresh water pump appears in the considered system, and challenges arise in regulating coolant temperatures under varying ambient conditions and engine loads. To address these challenges, the installation of shut-off valves will be necessary to ensure the connection of one ICC circuit with another cooling system circuit in appropriate modes. These valves are not depicted here as they are not activated in design mode. Whether the noted complications are worth the achieved reduction in M_Σ must be decided by the engine designer and manufacturer.

Thus, the smallest value of M_Σ was achieved in the E-type cooling system. It was reduced compared to the A-type cooling system by almost 30%. Next comes the type C cooling system scheme, which, in comparison with it, has an M_Σ increased by approximately 13%. At the same time, it has only one fresh water pump and is better adapted to changes in external temperature, as well as engine loads. Compared to the worst system, its M_Σ is reduced by 280 kg or 20%. Other systems are significantly worse.

4. Conclusions

The essence of this work was the ability to demonstrate improvement in the efficiency of the engine cooling system. Based on the analyses presented in the work, the following conclusions were drawn:

• The general patterns of reduction in M_Σ obtained for the simplest cooling system scheme should be considered as qualitative: in complex systems, other quantitative estimates apply.
• Achieving a minimum M_Σ in any cooling system occurs with a significant reduction in the flow of ICC through the heat exchangers, compared to the flow through the engine; therefore, the name “low-flow” for such cooling systems is quite logical.
• The change in M_Σ in the cooling system, when regulating ICC costs, depends on η₀, and the greater the higher η₀.
• Simultaneous minimization of all masses of the heat exchanger cores M_i in a complex system, when regulating the ICC flow rates to find the minimum M_Σ, does not occur: some Mi increase, others decrease.
• In various complex low-flow cooling systems, with the same engine parameters, different minimum values of M_Σ are possible. This depends on the conditions of using heat exchangers with the largest M_i in the cooling system: they must be placed in conditions of the greatest efficiency of their operation.
• For the researched, relatively complex, rational cooling systems, their total core masses M_Σ can be different for the same engine and at the same operating mode. Importantly, this difference turned out to be significant. As can be seen from Table 6, the M_Σ values of the lightest and heaviest of the systems can differ by approximately 35% with the same efficiency of these systems. Other systems occupy intermediate positions.