3D CFD Simulation of Twin Entry Turbochargers in an Engine Environment

Abstract

In this long term project the behaviour of a twin scroll turbocharger in an engine environment with pulsating boundary conditions is investigated. A complete three dimensional turbocharger fluid model is built including exhaust manifold, turbine and compressor housing as well as the complete runners. The turbine and the compressor side is coupled by a momentum equilibrium (and) the instantaneous rotational speed of the turbocharger is calculated for each timestep. This model is capable of analyzing both, the transient pulse efficiency, which is generated by the working cycle and the operating behavior, especially the overflow losses in a twinscroll turbine caused by pressure pulses.

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Introduction

The increasing demands on the reduction of fuel consumption of passenger cars and the reduction of climate relevant emissions e.g. CO₂, lead to a higher focus on smaller turbocharged engines, the so called downsizing effect. Downsizing means the increase of engine efficiency as well as the reduction of emissions by reducing the engine displacement volume while maintaining constant driving performance by the use of a turbocharger [1]. The combination of direct injection and variable camshaft timing together with turbocharging has become the key technology today to reduce fuel consumption of gasoline and diesel engines and to improve efficiency. Reduced friction and moving the relevant operating points to higher loads near the efficiency sweet spot lead to lower specific fuel consumption compared to natural aspirated engines. The energy of exhaust gas exiting the engine should be harnessed to the most efficient extend in order to achieve rapid responding behavior and a high low-end-torque. For this reason the interaction between the engine and the turbocharger needs to be investigated especially due to pulsation. The turbine manufacturer measures turbine maps on a stationary hot gas test bench. But when flow pulsation takes place, the turbine mainly exceeds outside its stationary maintained operating map range as the flow will be highly pulsatile which leads to a varying efficiency during the engine cycle. Knowledge of this transient behavior is necessary for further procedure.

With this in mind, the goal of early research into turbochargers was to quantify the unsteady performance and operating behavior of turbines. Palfreyman and Botas [2] used an explizit rotating turbine runner mesh in their 3D CFD calculations. The comparison between the unsteady turbine efficiency with the efficiency measured on a stationary test bench showed a slightly lower efficiency for the quasi-steady experiment. Lam and Robert [3] came almost to the same conclusion by using a static runner mesh with a multiple reference frame. Winkler et al. [4] investigated the unsteady performance of a twin entry turbine in an engine environment. A significant interaction between the two turbine scrolls was discovered. This interaction influenced the isentropic efficiency. Also Copeland et al. [5] as well as Müller et al. [6] calculated the unsteady performance of a twin entry turbine and compared the results to a steady flow analysis. A discrepancy between steady state and pulse efficiency of the turbine has been proved in their work. To characterize the flow conditions inside a twin scroll turbine was the goal of Brinkert et al. [7]. The authors took measurements with dissimilar pressure admission on the scrolls and introduced parameters to describe the appeared results which were further analyzed by three dimensional CFD calculations.

Theoretical Background

Within this work a qualitative prediction on the efficiency and behaviour of a twin entry turbine under pulsating conditions will be made. This chapter contains a short overview of the most important equations and physics behind turbine efficiency and velocity ratio. The efficiencies used in this work are based on isentropic adiabatic conditions. The states 3^∗ and 4^∗ describe the turbine housing inlet and the diffusor outlet. State 3^∗ is divided into scroll 1 and scroll 2 in case of a twin entry turbine. The points right in front of the turbine runner and behind it are named 3 and 4. The total to total isentropic turbine efficiency η _tt, 34 is the relation between total enthalpy drop Δ h _t and the isentropic total enthalpy drop Δ h _ts over the turbine, which is calculated by (1) [1] using total temperature T _t , total pressure p _t and the specific heat capacity c _p of the exhaust gas. The coefficient of expansion is here named γ. The total to static efficiency is to be calculated analogically with respect to different indices.

$$\displaystyle{ \eta _{tt,34} = \frac{\varDelta h_{t}} {\varDelta h_{ts}} = \frac{h_{t,3} - h_{t,4}} {h_{t,3} - h_{t,4s}} = \frac{1 -\frac{T_{t,4}} {T_{t,3}} } {1 -{\frac{p_{t,4}} {p_{t,3}} }^{ \frac{\gamma -1} {\gamma } }} }$$

(1)

The turbine blade speed ratio S, presented in (2), defines the ratio of the rotor inlet tip speed u and the isentropic velocity c _s , which is the velocity the flow would obtain if expanded in an ideal nozzle [1].

$$\displaystyle{ S = \frac{u} {c_{s}} = \frac{u} {\sqrt{2 \cdot c_{p } \cdot T_{t,3 } \left (1 -{ \frac{p_{t,4 } } {p_{t,3}} }^{ \frac{\gamma -1} {\gamma } }\right )}} }$$

(2)

Model Building

The turbocharger modeled in this work originates from a four cylinder Otto engine with direct injection and 1,998 cm³ volume of displacement. The engine produces 194 kW power and delivers a maximum torque of 353 Nm with a boost pressure of 2,320 mbar. The valve overlap in accordance to the twin entry turbine leads to a high low-end-torque reached by scavenging the residual gas out of the cylinder. The twin scroll turbocharger with asymmetric scroll alignment is connected to the engine by a four in two exhaust runner (see Fig. 1). Combined are the two outer cylinders 1 and 4 and the two inner cylinders 2 and 3 to one entry of the turbine and are merged immediately upstream the runner.

Computational Mesh

The resulting flow model from the introduced components is shown in Fig. 1. The computational domain extends from the inlet to the exhaust runner over the turbine including the internal wastegate up to the entrance of the catalitic converter on the exhaust side. Air-sidely the compressor is modeled from the short suction pipe up to the end of the volute. The computational mesh of the complete flow model consists of 1.75 million nodes. In Table 1 the rounded node numbers of all components can be found. The turbine runner as well as the compressor runner are discretized by hexaeder elements, the housings and the exhaust runner are meshed by tetraeder elements. The tip clear between blade and shroud is resolved by five layers. Figure 2 shows the computational mesh of a turbine and a compressor blade passage.

Fig. 1

Geometry of the three dimensional CFD model including the exhaust runner plus turbine and the compressor side. Cylinder 1+4 are connected to the outer, more bent scroll 2 and cylinder 2+3 are connected to the inner scroll 1

Table 1 Nodes of the components

Fig. 2

Computational mesh of the turbine runner blade passage on the left side and the compressor runner blade passage on the right side. The turbine runner consists of eight passages and the compressor runner consists of six passages. The tip clear is coloured in red

Physics

For solving the problem the software Ansys CFX in version 14.0 has been used for the reason of its high reputation in the turbomachinery field. There were no experimental data available for a validation. Relevant properties used in this model can be found in Table 2. The specific enthalpy of the exhaust gas is temperature dependent and derives from a look-up table. For the rotating turbine and the compressor runner an explicit mesh motion is used. The stationary and the dynamic meshes are connected every timestep by a general grid interface. All walls in this case are treated as adiabatic. This complete model is independent from turbine or compressor maps. The rotational speed of the rotor is calculated for each timestep by a momentum equilibrium between the turbine and the compressor side including the bearing friction with (3)–(5). The momentum difference M _difference is obtained by the sum of the momentum that the turbine delivers M _turbine , the momentum that the compressor transfers to the fresh air M _compressor and the friction momentum M _friction that is lost in the bearings. With this momentum difference an angular acceleration $\dot{\omega }$ is calculated and used to set the rotational speed for the next time step. The moment of inertia of the rotor J _TC in (4) amounts $2,30 \cdot 1{0}^{-5}\ kg \cdot {m}^{2}$. The friction torque is a rotation speed dependent quantity. Axial movement of the rotor and variations in oil temperature are not taken into account.

$$\displaystyle\begin{array}{rcl} & & M_{\mathit{difference}} = M_{\mathit{turbine}} + M_{\mathit{compressor}} + M_{\mathit{friction}}{}\end{array}$$

(3)

$$\displaystyle\begin{array}{rcl} & & \qquad \qquad \qquad \dot{\omega } = \frac{M_{\mathit{difference}}} {J_{TC}} {}\end{array}$$

(4)

$$\displaystyle\begin{array}{rcl} & & \qquad \qquad \omega \left (t + 1\right ) =\omega \left (t\right ) +\dot{\omega } \cdot \varDelta t{}\end{array}$$

(5)

Table 2 Simulation properties

Fig. 3

Inlet boundary conditions for the four exhaust runners. Massflow over crank angle for the engine operating points 1,500 rpm and 5,500 rpm full load

Boundary Conditions

The boundary conditions used in this work come from a one dimensional fluid model of the complete engine that delivers time-resolved data for massflow, temperature and pressure for both inlets and outlets of the turbocharger model. The operating point analyzed in this paper is full load at 5,500 engine rpm at the engine maximum power. The massflow $\dot{m}_{inlet}$ over crank angle for two operating points at the exhaust runner inlets is shown in Fig. 3. The compressor inlet boundary condition is ambient pressure at 300 K and it produces boost pressure against a static pressure of 0.4 bar upto 1.4 bar, depending on the engine operating point.

Simulation Results

In Fig. 4 the torque produced by the pressure forces of the exhaust gas on the turbine blades is displayed over crank angle. When substracting the torque the compressor transfers to the fresh air and the torque lost in the bearings from the turbine torque the difference torque remains, which is responsible for the dynamic change in the turbocharger’s rotational speed. As can be seen, the torque peaks from scroll 1 are higher than those from scroll 2. This can be explained by the either differently angled scrolls since a higher angle results in higher incidence losses.

Fig. 4

Resulting torques on turbine and compressor runner over crank angle. The difference torque which accelerates or decelerates the rotor is coloured in green. Above, the inlet massflows of the four exhaust runners are plotted in black for scroll 1 and in grey for scroll 2. The cutting plane through the turbine is shown at two peak points of torque. The left picture shows the scroll 1 active at 38^∘CA the right one shows scroll 2 active at 585^∘CA. The cutting planes are coloured with the tangentially projected velocity streamline vectors

Fig. 5

Rotational speed of the turbocharger n _TC at 5,500 engine rpm. Above, the inlet massflows into the four exhaust runners are plotted in black for scroll 1 and in grey for scroll 2

The difference torque results in rotational speed fluctuations of the turbocharger that are plotted over crank angle in Fig. 5. At the engine operating point of 5,500 rpm the turbocharger speed varies by 3,500 rpm with higher peaks for scroll 1 that delivers the higher torque to the rotor shaft. Further the phase shift of 57^∘CA in pressure pulse between the exhaust runner inlet and the resulting rotor accelerating can be observed.

Efficiency

With respect to (1) the adiabatic total to static turbine efficiency $\eta _{ts,{3}^{{\ast}}{4}^{{\ast}}}$ for each scroll over the complete turbine is plotted in Fig. 6. The diagram shows that the peaks for scroll 1 are about 10 % higher than for scroll 2. Due of the time shift between inlet and outlet conditions of the turbine, efficiencies over 1 can occur. An efficiency below 0 means an inactivity of the scroll or flowback into the exhaust runner. The averaged efficiency over four working cycles for scroll 1 is 53.1 % and 44.6 % for scroll 2. Further turbine blade speed ratio, that is plotted in Fig. 7, varies during the pulse cycle. The ratio rises to an optimum value of 0.7 when pressure pulse decreases and rapidly drops to 0.5 when again pressure pulse increases. It is quite visible that the turbine is mainly operating away from the optimum value of 0.7, further information can be found in [1].

Fig. 6

Total to static isentropic turbine efficiency $\eta _{ts,{3}^{{\ast}}{4}^{{\ast}}}$ at 5,500 engine rpm. Above, the inlet massflows of the four exhaust runners are plotted in black for scroll 1 and in grey for scroll 2

Fig. 7

Isentropic turbine velocity ratio ${}^{u}/_{c_{s}}$ at 5,500 engine rpm. Above, the inlet massflows into the four exhaust runners are pictured in black for scroll 1 and in grey for scroll 2

Transient Effects

Transient effects occur when the turbine works under pulsating conditions. The turbine charges when pressure pulse increases and discharges when pulse decreases. In Fig. 8 the instantaneous shaft power is plotted over the turbine runner inlet massflow $\dot{m}_{3}$. It can be observed that the turbine is charging from 0 to 30^∘CA. After peak massflow, the turbine is discharging until 180^∘CA. The shaft power, generated from the turbine, is up to 40 % higher for the discharging phase for the same turbine inlet massflow. So it can be assumed that there is a mass storage in the turbine, since different shaft powers for the same massflow are delivered. This mass storage influences the operating behaviour and the turbine can not be treated as quasi-stationary.

Fig. 8

Instantaneous shaft power over turbine runner inlet massflow $\dot{m}_{3}$ for scroll 1

Fig. 9

Twin scroll specific overflow factor. Cutting plane through the turbine is coloured with the velocity and shows tangentially projected streamline vectors. An overflow from scroll 1 in scroll 2 is shown. For each scroll a circumferential control surface has been defined. Its normal vectors are n _sf1 and n _sf2. While m _sf describes the complete massflow through the control surface, m _sf, in accounts for the massflow only in surface normal direction which is the massflow from the active scroll into the inactive one

Overflow Losses

The cutting plane in Fig. 9 shows the tangentially projected streamline vectors. An overflow from the active scroll 1 to the opposite one can be observed. Two circumferential control surfaces sf1 and sf2 in Fig. 9 are defined in order to calculate the massflow through each scroll. By the use of a surface normal vector n _sf an overflow massflow $\dot{m}_{sf,in}$ to the inactive scroll can be calculated by means of (6) and (7). To quantify the overflow losses, by means of the massflows $\dot{m}_{sf}$ and $\dot{m}_{sf,in}$, a specific number, namely the scroll overflow factor SOF is introduced and calculated for each scroll. The overflow determined by $\dot{m}_{sf,in}$ is considered as a loss of usable exhaust gas enthalpy since the overflown mass mainly flows back into the exhaust runner and cannot be converted into shaft power.

$$\displaystyle\begin{array}{rcl} v_{\mathit{normal}}& =& \mathbf{n}_{sf} \cdot \mathbf{ v}{}\end{array}$$

(6)

$$\displaystyle\begin{array}{rcl} \dot{m}_{\mathit{sf },\mathit{in}}& =& \int \limits _{sf}\rho \cdot v_{\mathit{normal}}dA{}\end{array}$$

(7)

$$\displaystyle\begin{array}{rcl} \mathit{SOF}_{\mathit{scroll}1}& =& 1 -\frac{\dot{m}_{sf1} -\dot{ m}_{sf2,in}} {\dot{m}_{sf1}} {}\end{array}$$

(8)

$$\displaystyle\begin{array}{rcl} \mathit{SOF}_{\mathit{scroll}2}& =& 1 -\frac{\dot{m}_{sf2} -\dot{ m}_{sf1,in}} {\dot{m}_{sf2}} {}\end{array}$$

(9)

In Fig. 10 the scroll overflow factor is shown over crank angle for each scroll. A higher SOF for scroll 2 can be observed. This behaviour matches the lower efficiency of the angled scroll shown in Fig. 6, which means also that there is a higher backflow into the exhaust runner through scroll 1.

Fig. 10

Scroll overflow factor SOF for each scroll over crank angle for engine operating at 5,500 rpm. Above, the inlet massflows into the four exhaust runners are plotted in black for scroll 1 and in grey for scroll 2

Backflow

In Fig. 11 the inlet and outlet massflows of the turbine housing are visualized with normally projected streamline vectors. It can be observed that the overflown mass from scroll 2 in the opposite one flows through the volute back into the exhaust runner. The backflow through scroll 1 is higher due to the higher overflow of the opposite scroll 2. The problem of this backflow is the negative influence on the gas exchange, especially at low engine speeds during valve overlap phase.

Fig. 11

Mechanism of exhaust gas backflow into the exhaust runner at 5,500 engine rpm. The cutting plane through the turbine volute shows the tangentially projected streamline vectors and an overflow from the active scroll 1 into the inactive one can clearly be seen. This overflown mass flows back into the exhaust runner

CPU Time

The Nec Nehalem Cluster of the Höchstleistungsrechenzentrum Stuttgart is used to solve this problem. Its CPUs are Intel Xeon (X5560) Quad Cores with 2.8 GHz and 12 GB memory. The node to node interconnection runs through an Inifiniband ethernet. In Fig. 12 the time per iteration in seconds is shown from eight CPUs in use up to 256 CPUs on the left side. On the right side there is shown the job time in days to run four engine cycles. The usage of 64 or 128 CPUs gives the best compromise, the calculation takes around six to seven days, starting off from a good initial solution.

Fig. 12

Job time in seconds to converge one iteration on the left and in days to converge four engine cycles on the right side

Conclusions

In this work the turbine behaviour under pulsating conditions was investigated. The instantaneous efficiency curve for the twin entry turbine for four workings cycles was plotted, the peak efficiency occurs at 390^∘CA for scroll 1. Time-averaged the scroll 1 shows a 7 % higher efficiency over the whole cycle than the opposite more angled scroll 2. In addition, an overflow from the active to the inactive scroll was detected. With respect to the efficiency curve the more angled scroll has a higher overflown massflow and hence a higher loss than scroll 1. A backflow of the overflown mass into the exhaust runner is a result of this overflow effect. In future the turbine efficiency and overflow factor will be investigated for low engine speeds. Additionally, different twin entry turbine designs, e.g. the dual volute will be compared to the standard twin scroll turbine. A design for delivering the best overall performance at low and high engine speeds, concerning efficiency, scroll overflow and resulting backflow is sought.