Study on Through-Flow Characteristics of a Diesel Two-Stage Supercharged Centrifugal Compressor under Variable-Altitude and Multiple Operating Conditions

Abstract

Understanding the influence of environmental boundary parameters on the through-flow characteristics of two-stage supercharged centrifugal compressors is the key to maximizing the power recovery potential of diesel engines at high altitudes. In this paper, the influence of the compressor through-flow characteristics on the full-load thermal cycle performance of a diesel engine under variable altitude is studied by means of tests and simulation. The results show that with the increase in altitude, the range of stable work flow decreases, and the pressure ratio of the plugging point changes greatly with altitude. The efficiency of the compressor with the same mass flow point decreases, and the highest efficiency point moves in the direction of the small flow range. With the goal of maximizing the torque of the diesel engine under full load and low speed, the key geometric parameters of the variable-altitude through-flow characteristics of the two-stage supercharged compressor were optimized as follows: at the altitudes of 0 m, 2500 m, and 5500 m, the diesel engine torque increased by 5.89%, 3.78%, and 2.18%, respectively. Based on the optimization method of the compressor through-flow design, a new direction is provided to break through the research on the independent limitation of the diesel engine thermal cycle performance optimization and compressor flow control.

1. Introduction

Plateaus with elevations above 3 km account for 25.9% of China’s total land area. Because a series of national and defense strategies, such as “the Belt and Road” and the China–India border, have been put forward, civil and military power equipment powered by diesel engines (transport vehicles, construction machinery, military vehicles, drones, etc.) is being widely used in these areas [1]. However, with the increase in altitude, the atmospheric pressure, temperature, and other environmental conditions continuously decrease, which leads to the deterioration of the power, economy, and reliability of the internal combustion engine working in the plateau region. The relevant studies show that the economy of the diesel engine decreases by 2.7~12.9% and that the dynamic performance decreases by 4.0~13.0% with each increase of 1000 m in altitude; CO, HC, and smoke emissions increase by 35%, 30%, and 34%, respectively [2]. Turbocharging is an important means of meeting the needs of internal combustion engines on plateaus. On the one hand, it can improve the intake density of internal combustion engines in a plateau region. On the other hand, due to the low exhaust back pressure in the plateau region, the turbine end expansion ratio increases and the turbine power capacity improves, which can further improve the engine performance [3]. However, a well-matched turbocharger at a fixed altitude and in fixed working conditions cannot take into account changing working conditions at different altitudes, and problems such as serious torque drop at low speed, turbine hysteresis, compressor surge, and efficiency decline often occur at high altitudes [4]. Therefore, advanced variable air-management systems such as variable cross-section supercharging (VGT) and two-stage adjustable supercharging are gradually being applied to high-altitude diesel engines. However, in the design process of the turbocharger, more attention is paid to single-stage efficiency, and a single design point at low altitude is often considered based on the assumption of steady flow; so, the internal unsteady flow field structure and flow mechanism are not fully studied [5,6,7].

The dual VGT two-stage adjustable supercharging system (VGT + VGT) refers to the use of the VGT system in both the high- and the low-pressure stages; the system has been used to improve the performance of diesel engines in variable-altitude areas [8]. Zhang Yangjun [9] from Tsinghua University compared and analyzed the fuel consumption rate of a diesel engine under the full load of 1000 r/min in three supercharging systems: the high-pressure-stage VGT, low-pressure-stage VGT, and double-VGT system. The results showed that the low-pressure-stage VGT could not reduce the fuel consumption rate of the diesel engine. Dual-VGT systems with high-pressure stages and bypass valves can achieve the best BSFC. VGT + VGT can integrate the advantages of the TST and the single-VGT system and represents the development trend of the two-stage supercharging system for vehicles in the future [10]. Compared with the single-stage turbocharger, the dual-VGT two-stage adjustable turbocharger system realizes the effective distribution of exhaust energy in the high- and low-pressure-stage turbines by adjusting the blade opening of the high- and low-pressure-stage VGT, which indirectly controls the speed of the turbocharger, and realizes the precise control of the booster pressure and intake flow to improve the comprehensive efficiency of the turbocharger system [11]. Although two-stage turbocharging and variable-section turbines can meet the measures of variable altitude by improving the utilization rate of exhaust energy at the turbine end, the improvement range and potential of the compressor end are constrained by the single-point matching condition, and the mismatch between the environmental factors and the turbocharger leads to the poor adaptability of the compressor at high altitudes [12].

As the altitude increases, the air flow inside the compressor enters the low Reynolds zone. As the gas density and temperature decrease at the same time, the effect of the viscous force gradually increases, and the compressor efficiency decreases [13]. Wu Gang [14] compared the influence of environmental boundary parameters (inlet temperature and inlet pressure) at 0 m and 4500 m altitudes, respectively, on the Reynolds number, and the results showed that the inlet temperature only changed the Reynolds number amplitude by 12%, while the inlet pressure changed the Reynolds number amplitude by 44%. The low exhaust back pressure and the high exhaust temperature of turbines in plateau areas increase the turbine expansion ratio, and the increased work done by the turbines leads to an increased compressor supercharging ratio [15]. Constrained by the single-point matching condition, the compressor blocking flow of the matching selection in the low-altitude operation condition of the internal combustion engine is relatively small [16]. When the vehicle is driving in the high-altitude area, the maximum power point of the internal combustion engine moves into the range of high speed and large flow, and the compressor overspeed and blocking tendency increase at the operating condition point [17]. The compressor with matching selection in the high-altitude operating conditions has a relatively large blocking flow. When the diesel engine with high-altitude matching works at low speed at a low altitude, the exhaust energy is larger, the trend of the maximum explosion pressure exceeding the limit is enhanced, the vibration is severe, and the mechanical load is increased. The reliability of the diesel engine is thereby reduced; the turbocharger will also appear to experience overspeed; the pressure ratio will be too large; and other problems will appear [18]. To sum up, the working conditions of a certain matching design point cannot meet the performance requirements of diesel engines with varying altitude and operating conditions. In particular, the change in the intake condition causes the deviation of the actual running line of the internal combustion engine and the matching running line of the compressor [19]. Under variable-altitude conditions, a mismatch will occur, leading to a significant decline in engine performance, economy, and other performance indexes. Therefore, it is necessary to conduct a detailed study of the problem of the poor adaptability to working conditions of centrifugal compressors in a two-stage turbocharging system within a certain height range. The research results have guiding significance for the optimization of the compressor structure and control strategy.

At present, Chinese internal combustion engine variable-altitude adaptability studies mainly focus on power recovery from low altitude to high altitude and pay more attention to experiments on the performance of the whole machine. The aerodynamic design level of the vehicle turbocharger is much lower than that of foreign countries and is far less mature than that of the domestic and foreign aviation engine industry. In the design process of the turbocharger, more attention is paid to single-stage efficiency, and a single design point is often considered based on the assumption of steady flow; so, the internal unsteady flow field structure and flow mechanism are not fully studied [20]. Because the flow in the turbocharger blade channel is in a state of nonlinearity and unsteadiness, there is a complex vortex structure. The adaptive turbocharging system experiences the mismatch phenomenon in the processes of variable-altitude working conditions, which leads to poor adaptability to the working conditions. Although measures such as two-stage supercharging and variable cross-section turbines have been developed in recent years, the exhaust energy utilization rate of the turbine end can be controlled through the valve adjustment of the turbocharger system or the adjustment of the turbocharger components to meet the requirements of variable altitude. However, the improvement range and potential of the compressor end are constrained by a single matching operating point, and the poor adaptability of the compressor caused by the mismatch of the turbocharger is still prominent. Therefore, it is necessary to start with the flow law of the compressor internal flow field to study the adaptability of the centrifugal compressor to variable altitude in the turbocharging system. It is helpful to monitor the influence of the gas path boundary parameters on the compression work and boost pressure of the variable-altitude two-stage compressor and to further improve the performance of the variable-altitude diesel engine.

The basis of the exploration of the mutual influence of the compressor through-flow characteristics on the thermal cycle performance of the diesel engine with a full load at variable altitude is the clarification of the compressor requirements when working at variable altitude. The diesel engine mainly controls the combined running line of the diesel engine and turbocharger through the turbine of the variable section of the high-pressure stage. When the full load of the supercharged diesel engine is running at a low speed, reducing the opening of the variable section can improve the pressure ratio and thereby improve the low-speed torque characteristics. The corresponding high-pressure centrifugal compressor running line is roughly parallel to the surge boundary. When the diesel engine speed rises to about 1000 r/min, the opening of the variable section is increased to reduce the exhaust resistance. The pressure ratio of the high-pressure centrifugal compressor tends to stabilize gradually with the increase in diesel engine speed, and it moves and extends towards the direction of the large flow range in order to make the running line pass through efficiently as far as possible. Because the two-stage compressor mainly relies on the high-pressure-stage compressor for pressurization when the speed is low, the low-pressure-stage compressor has low efficiency. When the diesel engine speed rises to about 1300 r/min, the LC is gradually switched to work, and the diesel engine torque slowly increases to the maximum torque point. Then, as the rotational speed increases, the opening of the high-pressure-stage turbine increases. At this time, the operation mainly relies on the low-pressure-stage compressor; the torque begins to decline, and the power rises to the rated power point.

The joint operation lines of the diesel engine and HC and LC can be obtained through simulation, as shown in Figure 1 and Figure 2, respectively:

It can be seen from Figure 1, Figure 2, Figure 3 that, with the increase in altitude, the joint running line of the diesel engine and the matched centrifugal compressor moves towards the direction of the large flow rate, high pressure ratio, and high speed. It can basically pass through the high-efficiency zone, but the LC efficiency is still low when the diesel engine is working at low speed, and the HC line is close to the surge boundary when the high altitude is 5500 m. Variable-altitude operating conditions require a wide range of the centrifugal compressor’s working flow; so, the stable working range should be expanded to make the surge boundary move to the direction of small flow as far as possible and to ensure that the low-speed, large torque point is far away from the surge boundary. The range of the high-efficiency zone should be increased so that the maximum torque point and rated power point (design matching point) are in the high-efficiency zone as far as possible. Therefore, it is of great significance to study the wide stability and high efficiency of the centrifugal compressor to improve the adaptability of the compressor to variable altitude.

In this paper, the influence of altitude on the altitude adaptability of the two-stage centrifugal compressor is analyzed based on the flow law of the internal flow field of the two-stage compressor. This article is divided into four parts. Firstly, the compressor requirements of a diesel engine with variable-altitude and full-load operation is introduced, and the matching simulation is carried out. Then, a test of the variable-altitude characteristics of the centrifugal compressor was carried out, and the changing law of the compressor pressure ratio characteristics and the efficiency characteristics was obtained under the conditions of variable altitude. A three-dimensional full-passage internal flow model of a two-stage supercharged centrifugal compressor and a one-dimensional thermodynamic cycle model of a two-stage adjustable supercharged diesel engine with a double VGT were established. The simulation research on the variable-altitude, multi-condition, through-flow operation was carried out jointly. Finally, aiming to optimize the maximum torque of the diesel engine under full-load and low-speed conditions, a compressor through-flow design optimization method based on the diesel engine under full load at variable altitude was proposed. On this basis, combined with the expansion and stability mechanism of the centrifugal compressor, a new technology for the flow control of the internal combustion engine was proposed by changing the key geometric parameters of the centrifugal compressor.

2. Experimental Facilities and Numerical Method

The experiment was carried out on the self-built, centrifugal compressor variable-altitude characteristics test bench, the layout of which is shown in Figure 4. In this paper, a six-cylinder V-type heavy-duty diesel engine is used to study the two-stage turbocharging system composed of KD76GCT and KD100GCT, which are newly matched and selected. The engine specifications are shown in

Table 1. Specifications of the engine.

Engine Parameters	Value
Type	V-type, supercharged and intercooled
Displacement (L)	8.6
Rated power (kW)/rotational speed (r/min)	258/2100
Maximum torque (N·m)/RPM (r/min)	1500/1300−150
Compression ratio	17:1
Ignition sequence	1-5-3-6-2-4
Cylinder diameter × stroke	112 × 145 (mm × mm)

.

The test bed of the characteristics of the variable-altitude centrifugal compressor simulates the plateau environment through an electric butterfly valve, a centrifugal pump, and air conditioning. The intake and exhaust manifolds are connected to the pressure-stabilizing box. According to the requirements of the different environmental parameters, the methods of electric butterfly valve intake throttling and centrifugal pump exhaust vacuuming are used to adjust the pressure in the inlet and exhaust pressure regulator boxes, so as to simulate the pressure of environmental media at an altitude of 0~5500 m. In this paper, representative altitudes are selected for the simulation tests. The pressures and temperatures corresponding to the four altitudes are shown in

Table 2. Inlet and exhaust environmental parameters.

Altitude (m)	Ambient Pressure (kPa)	Ambient Temperature (°C)
0	101	30
2500	75	22
3500	66	18
5500	50.5	10

.

In order to study the effect of altitude on the performance of the two-stage compressor, a pressure sensor and a thermal resistance temperature sensor are installed upstream of the intake manifold high-pressure-stage compressor (HC) and low-pressure-stage compressor (LC). The experimental settings are shown in Figure 5. The Kistler pressure sensor is installed downstream of the HC intake manifold, enabling real-time intake pressure data to be collected for model validation. The electromagnetic speed sensor is mounted on the volute of the compressor for easy recording of the turbocharger speed. A ZWRY-type bent-tube air flowmeter is installed downstream of the LC and records intake volume flow. All data acquisition and post-processing were performed using GT-SUITE v2020.2 software developed by Gamma Technologies. The test equipment information is shown in

Table 3. Test equipment information and parameters.

Name (Quantity)	Model Number	Main Measurement Parameters	Measurement Accuracy
Pressure sensor (8)	Piezoresistive pressure sensor	Inlet and outlet air pressure of compressor and turbine	±0.5%
Pressure transmitter (2)	Electric transmitter	Compressor outlet pressure, turbine inlet pressure	±0.08% FS
Temperature sensor (4)	Platinum thermal resistance sensor	Inlet and outlet air temperature of compressor and turbine	±0.5 °C
Temperature transmitter (2)	Thermal resistance isolated transmitter	Compressor outlet air temperature, turbine inlet air temperature	±0.2% FS
Flow sensor (2)	Twisted-wire flowmeter	Compressor outlet flow, turbine inlet flow	>1%
Tachometer sensor (1)	Non-contact magnetoelectric	Turbocharger speed	Not lower than the maximum measured value ± 0.2%

.

In addition to the test measurement, the numerical method is used to analyze the turbocharging system of the diesel engine in detail. The structure of the diesel engine model is shown in Figure 6, and the numerical simulation of the internal flow in the full-flow passage of the centrifugal compressor is shown in Figure 7. The model of the diesel engine is mainly based on the structural parameters of the test diesel engine and the parameters of the test system of the performance test at different altitudes. GT-ISE software was used to carry out the modeling and simulation of the one-dimensional thermal cycle. The press-ignition ternary Wiebe combustion model “DIWiebe” was chosen for the combustion model as it is commonly used to simulate the combustion and heat release of diesel engines [21].

The semi-empirical formula of “DIWiebe” model is derived from chemical reaction kinetics, as follows:

$$X=1-e^{-6.908{\left(\frac{\phi -{\phi }_a}{{\phi }_2}\right)}^{m+1}}$$

(1)

The derivative of both sides of this equation is taken with respect to φ:

$$\frac{dX}{\mathrm{d}\phi }=6.908\frac{m+1}{{\phi }_z}\cdot {\left(\frac{\phi -{\phi }_B}{{\phi }_z}\right)}^m\cdot {\mathrm{e}}^{-6.908{\left(\frac{\phi -{\phi }_c}{{\phi }_z}\right)}^{m+1}}$$

(2)

In the formula, $X$ is the percentage of fuel combustion; $dX/\mathrm{d}\phi$ is $X$ with the crank angle change rate; $m$ is the burning quality index; and $\phi ,{\phi }_z$, ${\phi }_B,{\phi }_C$ are the instantaneous crankshaft angle, combustion duration angle, combustion start angle, and combustion end angle, respectively. The combustion heat release rate expressed by this formula can be determined only by determining $m$, ${\phi }_z$, and ${\phi }_B$.

The overall mechanism of the centrifugal compressor includes a compressor impeller, a volute, and a diffuser. Vehicle centrifugal compressors mainly use a bladeless diffuser. The two centrifugal compressors numerically simulated in this paper were calculated by Army Military Transportation College and produced by Wuxi Kaidi Supercharger Parts Co., Ltd. (Wuxi, China). The models of the two-stage supercharged centrifugal compressors are the KD100GCT (low-pressure stage) and KD76GCT (high-pressure stage), respectively. The three-dimensional solid model is obtained by the reverse scanning of the product, and its basic mechanism parameters are shown in

Table 4. Structural geometric parameters of HC and LC.

Type	HC	LC
Number of blades	Eight main blades and eight shunt blades	Eight main blades and eight shunt blades
Impeller inlet diameter (tip)	52 mm	67 mm
Compressor inlet diameter	52.8 mm	68 mm
Axis length of impeller (tip)	21.76 mm	29.25 mm
Axis length of impeller (hub)	34.13 mm	37.25 mm
Working wheel outlet diameter	76 mm	100 mm
Diffuser outlet diameter	126 mm	176 mm
Working impeller outlet blade width	4 mm	5 mm
Outlet width of vaneless diffuser	3.5 mm	4.6 mm

.

Under the conditions of variable altitude, due to the difference in working conditions of the compressor and turbine, an equivalent and similar calculation of rotational speed and flow rate should be carried out. The correction formula is as follows:

$$RP{M}_{corrected}=RP{M}_{actual}\cdot \sqrt{\frac{T_{tef}}{T_i}}$$

(3)

$$m_{corrected}=m_{actual}\cdot \frac{P_{tef}}{P_i}\cdot \sqrt{\frac{T_i }{T_{tef}}}$$

(4)

In the above formula, $T_i$ is the inlet temperature of the compressor or the pre-vortex temperature of the turbine, and $T_{tef}$ is the reference temperature. For the compressor, $T_{tef}$ is the standard ambient temperature; $T_{tef}$ = 298 K, and for the turbine, $T_{tef}{=T}_i$; $P_{tef}$ is the reference pressure; the standard atmospheric pressure $P_{tef}=100 \mathrm{k}\mathrm{P}\mathrm{a}$ for the compressor, and $P_{tef}=P_i$ for the turbine.

The numerical simulation of the internal flow of a centrifugal compressor adopts computational fluid dynamics (CFD) to simulate the internal flow law of a centrifugal compressor with variable altitude [22]. The flow in a centrifugal compressor is mainly turbulent flow. Considering the complexity and calculation cost of the calculated object, the Reynolds mean numerical simulation was used to solve the N-S equation to obtain the numerical solution of the flow field [23]. For the solution, the dynamic viscosity coefficient μ and thermal conductivity κ are divided into laminar flow and turbulent flow, namely:

$$\mu ={\mu }_l+{\mu }_t$$

(5)

$$\kappa ={\kappa }_l+{\kappa }_t$$

(6)

where the turbulent dynamic viscosity coefficient is ${\mu }_t,\mathrm{a}\mathrm{n}\mathrm{d} {\mu }_l$ is the laminar viscosity coefficient.

$$\kappa =C_p\left(\frac{{\mu }_l}{P{r}_l}+\frac{{\mu }_t}{P{r}_t}\right)=\frac{\gamma R}{\gamma -1}\left(\frac{{\mu }_l}{P{r}_l}+\frac{{\mu }_t}{P{r}_t}\right)$$

(7)

In the calculation of ideal gas, the laminar Prandtl number $P{r}_l$ and turbulent Prandtl number $P{r}_t$ are 0.708 and 1.0, respectively. Therefore, solving $\mu$ and $\kappa$ can be reduced to solving ${\mu }_l$ and ${\mu }_t$ [24].

According to the empirical formula, ${\mu }_l$ can be obtained:

$$T_{\mathrm{\infty }}\ge 120 \mathrm{K},{\mu }_l\left(T\right)=\left\{\begin{array}{c}{\mu }_l\left(120\right)\cdot \frac{T}{120},(T\le 120 \mathrm{K})\\ {\mu }_l\left(T_{\mathrm{\infty }}\right)\cdot \left(\frac{T_{\mathrm{\infty }}+T_s}{T+T_s}\right)\cdot {\left(\frac{T}{T_{\mathrm{\infty }}}\right)}^{1.5},\left(T>120 \mathrm{K}\right)\end{array}\right.$$

(8)

$${T_{\mathrm{\infty }}\le 120 \mathrm{K},\mu }_l\left(T\right)=\left\{\begin{array}{c}{\mu }_l\left(T_{\mathrm{\infty }}\right)\cdot \frac{T}{T_{\mathrm{\infty }}},\left(T\le 120 \mathrm{K}\right)\\ {\mu }_l\left(120\right)\cdot \left(\frac{120+T_s}{T+T_s}\right)\cdot {\left(\frac{T}{120}\right)}^{1.5},\left(T>120 \mathrm{K}\right)\end{array}\right.$$

(9)

3. Results Analysis

3.1. Validation of the Numerical Method

The numerical model of the turbocharged diesel engine is verified by the test bed of the variable-altitude characteristics of the centrifugal compressor (Figure 8). By simulating the altitude conditions of 0 m, 2500 m, 3500 m, and 5500 m, the obtained simulation results of the full-load speed characteristics are compared with the existing test results, and the 5% error chart based on the test value is obtained. The simulated power of the diesel engine at the altitudes of 0 m and 2500 m is in good agreement with the experimental data. Although there is some degree of error in the performance simulation and test results for 3500 m and 5500 m, the error between the simulation results and the test values is within 5%, and the variation trend of both is consistent. It can be seen that the model can predict the effect of altitude on diesel engine performance well.

The flow field simulation and verification of the established centrifugal compressor full-passage internal flow model were carried out. The simulation results of the near-surge point, high-efficiency point, and plugging point at the HC 100,000 r/min and 120,000 r/min rotational speeds at a standard altitude were checked with the test data. The curve of the HC outlet pressure, pressure ratio, and efficiency changing with the flow rate is shown in Figure 9. The corresponding results of the LC at 70,000 r/min and 90,000 r/min are shown in Figure 10. It can be seen from the comparison curve in the figure that the calculation results of the outlet pressure and pressure ratio of the HC and LC have high accuracy and that the results are kept within 5% of the allowable error. However, since the calculation model was set as an adiabatic model in the simulation calculation, there were errors between the efficiency calculation results and the experimental data, but the variation trend was still consistent, and the model could meet the requirements for the subsequent analysis of the internal flow field of the two-stage centrifugal compressor.

By comparing the predicted values given above with the measured ones, it is concluded that the numerical model of the variable-altitude turbocharged diesel engine and the numerical simulation of the internal flow in the full-flow passage of the centrifugal compressor are reliable in predicting the performance of the diesel engine and the internal flow parameters of the two-stage compressor at different altitudes. Therefore, the detailed analysis below is credible.

3.2. Variable-Altitude Characteristics of Two-Stage Compressor

The foundation and the key to the improvement of the adaptability of the supercharged diesel engine to variable altitude lie in the rational optimization design of the centrifugal compressor to expand stability and increase efficiency flow. The altitude has an obvious influence on the characteristic curves of the two compressors; this influence can be reflected in the pressure ratio and efficiency-flow curves.

The pressurization ratio is one of the most critical aerodynamic performance parameters of centrifugal compressors; it is used to characterize the pressurization degree of the compressors. It can be calculated as follows:

$${\pi }_c=\frac{P_k}{P_a}$$

(10)

where $P_k$—compressor outlet pressure and $P_a$—compressor inlet pressure, expressed by atmospheric pressure, when the compressor inlet flow loss can be ignored.

The adiabatic efficiency of the compressor can be calculated as follows:

$${\eta }_c=\frac{H_s}{H}=\frac{\frac{K}{K-1}R{T}_a\left[{\left({\pi }_c\right)}^{\frac{K-1}{K}}-1\right]}{\frac{K}{K-1}R\left(T_k-T_a\right)}=\frac{T_a\left[{\left({\pi }_c\right)}^{\frac{K-1}{K}}-1\right]}{T_k-T_a}$$

(11)

where $H$—the total work of the compressor; $K$—adiabatic index of air, $K=C_P/C_V$; 1$R$—gas constant, gas constant of air R = 287 J/kg·K; $T_a$—compressor inlet temperature; and $T_k$—compressor outlet temperature.

Reduced flow $m_c$ is calculated as follows:

$$m_c=m\frac{P_c}{P}\sqrt{\frac{T}{T_c}}=m\frac{100}{P}\sqrt{\frac{T}{298}}$$

(12)

The main performance indexes of the centrifugal compressor flow characteristics include boost ratio, adiabatic efficiency, and flow rate. As the altitude increases, the Reynolds number of the gas flowing through the impeller decreases and the influence of viscous resistance increases, which changes the flow loss inside the impeller and thus makes the compressor characteristic curve change with the altitude. Figure 11 and Figure 12 show the comparison of the pressure ratio characteristics of the HC and LC measured by tests under simulated intake conditions at different altitudes.

It can be seen from Figure 11 and Figure 12 that when the altitude increases, that is, when the ambient pressure and temperature of the intake air decrease, the mass flow rate at the same measurement condition point decreases. The compressor’s stable working flow range shrinks and moves towards the small flow range, which is conducive to the movement of the joint running line of the diesel engine and compressor towards the small flow range under the condition of altitude change; thus, it can maintain a sufficient surge margin and ensure that the diesel engine’s low-speed torque can work stably. The surge point pressure ratio changed little before and after altitude change, but the plugging point pressure ratio changed greatly with altitude. Compared with the altitude of 0 m, the plugging point pressure ratio of the high-pressure compressor increased by 16.21% and 22.67% at 2500 m and 5500 m, respectively, while the plugging point pressure ratio of the low-pressure compressor increased by 14.96% and 24.66% at 2500 m and 5500 m, respectively.

It can be seen from Figure 13 that when the altitude increases, that is, when the intake ambient pressure and temperature decrease, the corresponding efficiency of the HC and LC with the same mass flow rate decreases. However, under the same rotational speed, the maximum efficiency point moves in the direction of the small flow range. The main difficulties restricting the work of the diesel engine with the change in altitude are the surge point and the highest efficiency point; so, under the condition of maintaining the same pressure ratio and intake temperature, if the altitude increases and the efficiency decreases then the exhaust temperature increases and the efficiency of the diesel engine working at high altitude and low speed is low. At the same time, the exhaust energy corresponding to the maximum torque point of the diesel engine at the highest efficiency point of the compressor is insufficient under the high-altitude conditions, and the efficiency of the compressor end reduces the intake volume, which further worsens the performance of the diesel engine.

It can be seen from the comparison that with the increase in the altitude, the stable working flow range of the secondary compressor narrows and moves in the direction of the small flow, and the pressure ratio of the plug point changes greatly with the altitude. The efficiency of the compressor with the same mass flow point decreases, and the highest efficiency point moves in the direction of the small flow range under the condition of the same speed. Therefore, an important direct conclusion is that the optimization of the two-stage compressor system needs to improve the internal flow field of the compressor. When the HC and LC operate in the optimized area at the same time, the compressor stability and efficiency can be improved by reducing the secondary flow between the impellers, the fluid turning loss, and the clearance loss.

3.3. Internal Flow Law and Performance of Two-Stage Compressor under Variable Altitude

Based on the requirements of diesel engines for compressors under variable-altitude conditions and the variable-altitude characteristics of two-stage compressors, combined with the numerical model of the internal flow in the full-flow passage of two-stage centrifugal compressors, the influence of the internal flow law and the performance of two-stage compressors under the typical conditions of variable altitude can be obtained, and the changing mechanism of the compressor flow field under variable-altitude conditions can be deeply analyzed. In this paper, the calculation iteration steps of nine calculation conditions are set to 1000 steps; the total calculation time is more than 36 h; and the calculation results can basically ensure convergence. This paper aims to explore the internal flow field of two-stage supercharged centrifugal compressors at different elevations; it mainly considers the impeller dynamic pressure distribution and the relative Mach number distribution of the 90% blade height section of the impeller. The following are the nine calculation results of the low-speed and high torque point, the maximum torque point, and the rated power point under the full-load conditions of the diesel engine at the three altitudes of 0 m, 2500 m, and 5500 m, respectively.

Figure 14 and Figure 15 show the comparison of the static pressure of the volute of the LC and HC under different typical working conditions of the full load of the diesel engine at different altitudes. It can be seen that the static pressure from the inlet to the outlet of the vaneless diffuser increases in general. Among them, after the gas passes through the diffuser, the kinetic energy is converted into pressure energy; so, the static pressure at the diffuser increases rapidly. According to the density of the contour line, the static pressure increase in the rated power point is the largest, followed by the maximum torque point; the low-speed, high torque point is the smallest. Because the structure at the exit of the volute is gradually expanding, the static pressure drops slightly. The LC volute outlet can achieve the maximum static pressure at the maximum torque point, and the HC volute outlet can achieve the maximum static pressure at the rated power point. The maximum static pressure achieved by the volute static pressure of the HC is higher than that of the LC. The static pressure of the volute decreases with the increase in altitude. The LC maximum torque point and the rated power point of the volute static pressure drop is larger at the low-speed, high torque point; the drop degree of the HC’s typical working condition point is similar.

The relative Mach number is often used to characterize velocity in a velocity field distribution cloud. Figure 16 and Figure 17 show the comparison of the relative Mach number of the 90% blade height section of the HC and LC at the typical full-load operating points of diesel engines at different altitudes. For the LC, the low-speed area of the blade flow field expands to the upstream direction of the clearance between the main blade and the shunt blade at the low-speed, high torque operating point. With the increase in altitude, the lowest velocity region is concentrated towards the suction side of the main blade. The relative Mach number of the low-velocity fluid at 2500 m is significantly less than that at the other two altitudes, and the flow velocity is faster at the blade root on the pressure side of the blade. At the maximum torque point, the low-speed area of the blade flow field also expands to the upstream direction of the clearance between the main blade and the shunt blade. The point of low speed and high torque in the low-speed zone is elongated. With the increase in altitude, the fluid velocity increases more than the point of low speed and high torque, and the area of high-speed fluid expands and is mainly concentrated at the tip and root of the pressure side of the main blade.

For high-pressure-stage compressors, under low-speed and high torque conditions, the lowest velocity area of the blade flow field is concentrated at the pressure side tip of the diverter blade. The average flow velocity of fluid at a 2500 m altitude is higher than that at the other two altitudes, and there is a small transonic flow area at the suction side blade root of the main blade and the diverter blade. At the maximum torque point, the average flow velocity of the fluid is larger than that at the low-speed and high torque point. With the increase in altitude, the area of the high-speed fluid at the root of the suction side of the blade increases. There is basically no low-speed fluid with a relative Mach number less than 0.4 in the impeller under the rated power point conditions, and the flow velocity through the impeller is larger than that under the other two conditions. A large number of transonic flow areas appear in the suction side blade root of the main blade, and their areas increase with the increase in altitude.

In summary, it can be concluded that at different typical operating points, the variation in the low-velocity fluid area is elongated with the increase in altitude, while the area of the high-speed fluid area increases with the increase in altitude. The flow-loss area of the LC impeller is concentrated when the rated power of the diesel engine is running at high altitude. The flow loss of the high-pressure compressor impeller is mainly concentrated at the low-speed and high torque points at low altitude. Therefore, it is necessary to optimize the key geometric parameters of the compressor flow characteristics under variable-altitude and multiple operating conditions based on the above two points.

3.4. Compressor Through-Flow Design Optimization

The related research given above describes the influence of the compressor through-flow characteristics on diesel engine full-load performance at variable altitude, and it provides the analysis of the internal flow field of the two-stage supercharged compressor under typical working conditions. In order to reduce the flow loss in the tip area of the low-pressure compressor impeller at the rated power point of the diesel engine at high altitude, this paper intends to optimize the inlet tip blade angle ${\beta }_{1l}$ to obtain the best intake angle and to reduce the fluid turning loss. In view of the phenomenon of the large flow loss range of the high-pressure compressor impeller under low-altitude conditions, this paper intends to optimize the ratio of the maximum inlet diameter of the high-pressure compressor impeller to the outer diameter of the impeller $D_{1h}/D_{2h}$ to control the influence of the Ge-type force generated when the impeller is rotating on the fluid flow. The key geometric parameters of the variable-altitude through-flow characteristics of the two-stage booster compressor are determined as follows: the bending angle after the outlet of the low-pressure compressor impeller ${\beta }_{2l}$, the angle of the inlet tip blade ${\beta }_{1l}$, and the ratio of the maximum inlet diameter of the high-pressure compressor impeller to the outer diameter $D_{1h}/D_{2h}$.

(1)

Full-load low-speed condition

This is determined in order to ensure that the diesel engine can have high low-speed torque and good transient response characteristics when working under full-load and low-speed conditions at high altitude. By determining the torque T_q of the diesel engine under certain low-speed conditions at high altitude, the torque reaches the maximum as the optimization objective of the compressor design. The objective function is defined as:

$$\mathit{max}{F}_1=f_{T_q}({\beta }_{2l},{\beta }_{1l},\frac{D_{1h}}{D_{2h}})$$

(13)

(2)

Full-load high-speed condition

This is conducted in order to make the diesel engine under full-load, high-speed working conditions have high calibrated power. Therefore, the rated power $P_e$ of the diesel engine at a certain high-speed condition was determined to achieve the maximum as the optimization objective of the compressor design. The objective function was defined as:

$$\mathit{max}{F}_2=f_{P_e}\left({\beta }_{2l},{\beta }_{1l},\frac{D_{1h}}{D_{2h}}\right)$$

(14)

Figure 18 shows the comparison of the external characteristics and performance of the dual-VGT adjustable two-stage supercharged diesel engines at different altitudes. As can be seen from the figure, with the increase in altitude, the decline in the diesel engine’s low-speed, large torque point is improved. At the altitude of 5000 m, when the diesel engine speed is 1200 r/min, the low-speed, large torque point only decreases by 7.72% compared with 0 m. The maximum torque point of the diesel engine decreases by 7.91% when the rotational speed is 1500 r/min. With the increase in the altitude, the lowest fuel consumption rate of the diesel engine at 1200 r/min at the altitude of 5000 m is 8.06% higher than that at 0 m, and the lowest fuel consumption point of the diesel engine moves in the direction of low speed.

As can be seen from Figure 19, the maximum torque at the point of diesel engine operation at variable altitude and low-speed and high torque is optimized, and the results show that at the altitude of 0 m, 2500 m, and 5500 m, the torque of the optimized compressor diesel engine increases by 5.89%, 3.78%, and 2.18%, and the volumetric efficiency increases by 35.28%, 21.84%, and 14.51%, respectively. Fuel consumption under the maximum torque condition is reduced by 2.89%, 2.80%, and 0.53%, respectively. The rated power under the operating conditions is reduced by 1.63%, 1.05%, and 1.28%, respectively.

4. Conclusions

Diesel engine performance deteriorates obviously at high altitude. Turbocharging, as an important technical means of meeting the requirements of diesel engines working at high altitude, has attracted much attention from researchers. It is of great significance to understand the characteristics of two-stage compressors at different elevations for the optimization and regulation of compressor architecture. In this paper, the flow field analysis method, combining experimental and numerical calculation, is used to study the interaction between the full-load performance of a heavy diesel engine at variable altitude and the compressor through-flow characteristics. Four main conclusions can be drawn from the study:

(1)

Variable-altitude environmental boundary conditions require a wide range of the centrifugal compressor’s working flow; so, the stable working range should be expanded to make the surge boundary move in the direction of the small flow as far as possible and to ensure that the low-speed, large torque point is far away from the surge boundary. The range of the high-efficiency zone should be increased so that the maximum torque point and rated power point (design matching point) are in the high-efficiency zone as far as possible.

(2)

The pressure ratio of the surge point changes little before and after the change in altitude, but the pressure ratio of the plugging point changes greatly with altitude. Compared with the altitude of 0 m, the plugging point pressure ratio of the high-pressure compressor increases by 16.21% and 22.67% at 2500 m and 5500 m, respectively, while the plugging point pressure ratio of the low-pressure compressor increases by 14.96% and 24.66% at 2500 m and 5500 m, respectively.

(3)

The static pressure of the volute decreases with the increase in altitude. The LC maximum torque point and rated power point volute static pressure drop is larger at the low-speed and large torque point; the point drop degree of the HC’s typical working conditions point is similar.

(4)

With the maximum low-speed torque of the diesel engine under full load as the optimization objective, the torque increases by 5.89%, 3.78%, and 2.18%, respectively, at the altitudes of 0 m, 2500 m, and 5500 m.

The research results have a certain guiding significance for the optimization of compressor performance and the improvement of diesel engine adaptability under variable-altitude conditions. This paper is based on the study of the internal flow field of the centrifugal compressor in the turbocharging system with variable-altitude and multiple operating conditions. When combined with the requirements of diesel engine variable-altitude operation for compressor performance, the restriction caused by the diesel engine thermal cycle performance optimization and the compressor flow control being independent of each other is reduced. A design method to implement a compressor through-flow based on the variable-altitude full-load working requirements of the diesel engine was developed to optimize the performance of the diesel engine.