1D engine simulation of a turbocharged SI engine with CFD computation on components

Transcription

1 1D engine simulation of a turbocharged SI engine with CFD computation on components Ulrica Renberg Licentiate Thesis Department of Machine Design Royal Institute of Technology S Stockholm TRITA-MMK 2008:09 ISSN ISRN KTH/MMK/R-08/09-SE

2 TRITA-MMK 2008:09 ISSN ISRN/KTH/MMK/R-08/09-SE 1D engine simulation of a turbocharged SI engine with CFD computation on components Ulrica Renberg Licentiate thesis Academic thesis, which with the approval of Kungliga Tekniska Högskolan, will be printed for public review in fulfillment of the requirements for a Licentiate of Engineering in Machine Design. The public review is held at Kungliga Tekniska Högskolan, Brinellvägen 64 in room M3 at 10:00 AM on the 5 th of September 2008.

3 Abstract Techniques that can increase the SI- engine efficiency while keeping the emissions very low is to reduce the engine displacement volume combined with a charging system. Advanced systems are needed for an effective boosting of the engine and today 1D engine simulation tools are often used for their optimization. This thesis concerns 1D engine simulation of a turbocharged SI engine and the introduction of CFD computations on components as a way to assess inaccuracies in the 1D model. 1D engine simulations have been performed on a turbocharged SI engine and the results have been validated by on-engine measurements in test cell. The operating points considered have been in the engine s low speed and load region, with the turbocharger s waste-gate closed. The instantaneous on-engine turbine efficiency was calculated for two different turbochargers based on high frequency measurements in test cell. Unfortunately the instantaneous mass flow rates and temperatures directly upstream and downstream of the turbine could not be measured and simulated values from the calibrated engine model were used. The on-engine turbine efficiency was compared with the efficiency computed by the 1D code using steady flow data to describe the turbine performance. The results show that the on-engine turbine efficiency shows a hysteretic effect over the exhaust pulse so that the discrepancy between measured and quasi-steady values increases for decreasing mass flow rate after a pulse peak. Flow modeling in pipe geometries that can be representative to those of an exhaust manifold, single bent pipes and double bent pipes and also the outer runners of an exhaust manifold, have been computed in both 1D and 3D under steady and pulsating flow conditions. The results have been compared in terms of pressure losses. The results show that calculated pressure gradient for a straight pipe under steady flow is similar using either 1D or 3D computations. The calculated pressure drop over a bend is clearly higher using 1D computations compared to 3D computations, both for steady and pulsating flow. Also, the slow decay of the secondary flow structure that develops over a bend, gives a higher pressure

4 gradient in the 3D calculations compared to the 1D calculation in the straight pipe parts downstream of a bend. Keywords: 1D modeling, CFD modeling, turbine efficiency, pipe flow, turbocharged engine 2

5 Contents 1. INTRODUCTION OBJECTIVES SOME ASPECTS OF TURBOCHARGED ENGINES BACKGROUND TO CURRENT ENGINE SIMULATION TOOLS TURBOCHARGER STEADY FLOW PERFORMANCE TURBOCHARGER QUASI-STEADY PERFORMANCE MODELING ADEQUATENESS OF QUASI-STEADY APPROACH PERFORMANCE DATA TURBINE BEHAVIOR UNDER STEADY AND UNSTEADY FLOW ASSESSMENT OF FLOW UNSTEADINESS THEORETICAL BACKGROUND GOVERNING EQUATIONS D MODELING ENGINE SIMULATION MODEL STRUCTURE MODELING OF FLUID FLOW Discretization method Pipe flow Straight pipe Bent pipe Flow split ENGINE CYLINDER Combustion model Engine cylinder valves TURBOCHARGER Performance maps NUMERICAL COMPUTATION OF TURBULENT FLOWS BASIC CONSERVATION EQUATIONS TURBULENT FLOWS AND THEIR MODELING Eddy Viscosity Models BOUNDARY CONDITIONS Turbulent flow boundary conditions Wall boundary conditions INLET CONDITIONS DISCRETIZATION Spatial discretization of the convective term Temporal discretization Discretization error estimation SOLUTION ALGORITHM COUPLED 1D & 3D SIMULATION TOOL

6 3.5.1 BOUNDARY INTERFACES TIME STEPPING EXPERIMENTAL METHOD ENGINE IN TEST CELL MEASUREMENT METHODS Pressure Temperature Mass flow rate Turbocharger speed RESULTS ENGINE MODELING CALIBRATION INSTANTANEOUS TURBINE EFFICIENCY ACCURACY OF THE CALCULATED TURBINE EFFICIENCY CFD MODELING OF PIPE FLOWS METHODS BENT PIPE GEOMETRIES Steady flow Three-dimensional CFD results compared to 1D Pulsating flow Full CFD results compared to 1D EXHAUST MANIFOLD Steady flow CFD results compared with 1D results Pulsating flow Flow in manifold versus 1D INTEGRATED 1D/3D SIMULATIONS EXPERIMENTAL RESULTS OPERATING CONDITIONS MEASUREMENT ACCURACY SUMMARY AND CONCLUSIONS D COMPUTATIONS CFD COMPUTATIONS COMPARISON OF 1D AND 3D COMPUTATIONS FUTURE WORK ACKNOWLEDGEMENT NOMENCLATURE REFERENCES

7 10. APPENDIX

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9 1. Introduction A future demand for the SI engine is to increase its efficiency to meet the requirements of lower fuel consumption and CO 2 -emissions. It is especially important in the low load region where the SI engine has large pumping losses due to throttling. Main stream developments are downsizing and stratified combustion. Downsizing is equivalent to reducing the displacement volume of the engine and has the effect of decreasing the engine s pumping and frictional losses. Having the engine run at low speed allows these losses to be reduced even further. In addition, the operating point of a smaller engine is shifted towards higher load, resulting in higher efficiency due to the increased break mean effective pressure (BMEP). For acceptable drivability the downsized engine must be combined with an effective boosting system. The advanced charging system must maintain a high specific power, show good low end torque performance and also have fast transient response. For the SI engine the most promising solution to reduce fuel economy while keeping emissions very low is to combine a small displacement volume with technologies as turbocharging, direct injection and variable valve actuation. A potential increase in efficiency between % can be attained [17,19]. Some examples of advanced turbocharging technologies under development for downsized SI engine applications are electrically driven waste-gate valves, twin-entry turbine housings, variable geometry turbines (VGT), and VGT mechanisms. To manage a theoretical optimization of an advanced turbocharging system today's engine simulation techniques need further improvement. Since CFD modeling of the whole engine is not feasible 1D codes are frequently used to optimize complex boosting systems for improved engine performance. Still, a 1D flow assumption through these components may not be sufficiently accurate for component optimization. On-engine measurements are required for model calibration as their predictive performance is limited. The flow through the turbine is heavily pulsating and yet is it modeled with the use of steady flow performance maps and the assumption of quasi-steady behavior. The performance data used are also very sparse, especially for low mass flow rates and turbine pressure ratios and often does not cover the entire operating range of the heavily pulsating flow the on-engine turbine is exposed to. The inappropriateness of the quasi-steady modeling has been emphasized by several researchers. Continuing research work is needed in the field of onengine turbocharger performance to get a deeper knowledge of the unsteady flow behavior and how it differs from that of the steady flow case as is assumed in the 1D model. Better knowledge in 5

10 this area will allow improved accuracy of the 1D engine simulations which are very beneficial not the least for their flexibility and their low computing cost. In the pursuit of improving today s engine simulation techniques, sub-models for different components, such as the turbine, the inlet or exhaust manifold must be revised. Secondary flow effects in the exhaust manifold affect the instantaneous turbine performance as the turbine is mounted directly downstream of it. Large Eddy simulations (LES) on a radial turbine showed that both small and large scale perturbations at turbine inlet were shown to deteriorate the turbine shaft power [28]. This project has been focused on two issues: o Instantaneous turbine efficiency calculations using 1D engine simulation techniques. o Flow modeling in pipe geometries representative to those of an engine exhaust manifold. The first part included work that is an attempt to assess the discrepancies between the instantaneous turbine efficiency calculated from on-engine measurements and that from using the quasi-steady approach with steady-flow performance maps. Two different turbochargers were considered and the operating points were in the closed waste gate region. The second part concerned modeling of gas flow through single and double bent pipe geometries using one dimensional engine calculations and CFD, both under steady and pulsatile flow conditions. The reason for studying bent pipe geometries is that the exhaust manifold easily can be represented as a set of bends and junctions. The modeling of the latter component will be a part of the continuing project. A better understanding of how the 1D simulation tool treats the flow through complex geometries as the manifold and how that differs from the 3D flow calculation is important in trying to improve the predictive quality of the engine calculations. In this case, improvement by means of providing better inlet conditions to the turbine sub model. The first part of the work shows upon the restricted predictive property of the 1D engine simulation tools, in essence due to the limitations of the turbine performance modeling. To draw any bigger conclusions from the results, comparing the calculated instantaneous turbine efficiency 6

11 from measurements and from 1D engine simulation, high frequency measurements of mass flow rate and temperature must be performed; simulated values were used in this case. The second part of the work is aimed at contributing to an insight of the affects of the 1D assumption through engine components. This is done studying the secondary flow structures as these are obtained from 3D CFD calculations of the same problem set-ups. It is not trivial to convert a complex 3D geometry into a corresponding 1D model. The 3D computations on an exhaust manifold indicated the presence of a time-dependent and strong secondary flow. Additionally, an intermittent backflow was observed. Both these effects could cause deterioration of the turbine power output as compared to ideal inflow conditions to the turbine. Hand in hand with the development of improved engine simulation techniques comes the need for advanced measurement techniques for on-engine applications as well. The very harsh environment in the engine exhaust system puts severe demands on the measuring devices to be used there Objectives The objectives are: o To assess the accuracy of the simulated quasi-steady turbine performance by on-engine experiments The method used for this objective is to compare the calculated instantaneous turbine efficiency based on high frequency measurements of pressure and turbine shaft speed with simulated values using performance maps. Measurements and simulations were performed on two different turbochargers in the closed waste gate region o To assess and identify inaccuracies in the 1D engine simulation model when applied to engine manifolds and in particular to bent pipes. 1D engine simulations were performed on single and double bent pipe geometries as well as on the two outer runners of an exhaust manifold under steady and pulsatile flow. The results are assessed by comparing, in terms of losses, to full 3D CFD results for the same geometrical configuration and flow conditions. 7

12 o To assess the feasibility of carrying out a coupled 1D engine simulation and CFD calculations of the exhaust manifold and thereby retain 3D accuracy but with lower computational costs. The basic idea is that the coupling may enable the advantages of both approaches and eliminating the corresponding drawbacks. Since the 3D calculations are heavy and require long turn-over time, there is a basic interest in reducing that time while maintaining the accuracy. So far this aspect is not yet completed and only initial data is available in this thesis. 8

13 2. Some aspects of turbocharged engines 2.1. Background to current engine simulation tools One drawback with today s commonly used 1D engine simulation tools of turbocharged engines is their restricted predictive qualities. This is in particular true for the calculated turbine power which often must be adjusted with special efficiency and mass multipliers to get simulated results close to measured values. There is a strive for an improved turbine sub-model that can describe the turbine behavior under on-engine like conditions, characterized by very hot and pulsating flow, yet with low computing effort. There are a number of issues connected to the present turbine modeling procedure and even doubts about its adequateness, from the fundamental concept of treating the turbocharger as a quasi-steady flow device, using measured steady flow performance data to describe the turbocharger behavior, to the sparsity of the measured data provided by the turbocharger manufacturer. Measured data usually do not cover the entire operating range of the turbo for on-engine applications. The erroneously predicted turbine power will depend on the accuracy of the provided inlet conditions, i.e. simulated conditions at the outlet of the exhaust manifold. Depending on the sensitivity of the turbine model to inlet disturbances these inaccuracies may be important for the overall engine output results. A justifiable area to investigate is therefore how well the gas flow through complex geometries as the exhaust manifold is modeled. This type of geometry consists of bent pipes and flow splits where multidimensional effects as propagating pressure waves are reflected and transmitted at junctions, pipe ends etc. and secondary flow structures are developed. The accumulation on the blade outlet shroud (on the suction side) of low energy fluid, which comes from the internal secondary flows, gives rise to the increased losses at the rotating turbine blades. This was the conclusion from comparing Laser Doppler Velocimetry measurements of the internal flow through a radial turbine together with CFD analysis. Measurements and simulations showed good agreement [33]. Despite the multidimensional nature of the flow processes taking place in manifold geometries, 1D engine calculations are commonly used to optimize the influence of these systems on the engine performance. The simulation accuracy is restricted by the 1D flow assumption together with the use of semi-empirical correlations for the pressure loss and flow discharge coefficients. This way of modeling the exhaust manifold may not be sufficiently accurate for component optimization or 9

14 applicable for predictive engine simulations. Although correction factors are used in the 1D code to account for multidimensional flow effects, CFD calculations modeling the fluid turbulence through these types of geometries would be more accurate [22, 23, 27]. CFD modeling of the whole engine is not feasible due to the huge need for computational resources. Unfortunately, this situation will not be changed in the foreseeable future. Therefore, one has to restrict full CFD calculations to individual components or at most a couple of components. A way to improve engine calculations, within the limitations of computational resources, is to limit the CFD calculations to certain components and either integrate these with a 1D model of the rest of the engine or to improve the correction factors used in nowadays 1D engine codes. In a coupled 1D/3D calculation the discharge and pressure loss coefficients were determined and applied to an intake plenum of a turbocharged DI Diesel engine and used in a stand alone 1D model of the same engine at full load conditions. The coupled procedure gave a slight improvement of the accuracy of the simulated results. It is presumed that constant coefficients used in 1D engine simulation codes cannot be used to capture complex transient phenomena [23] Turbocharger steady flow performance A common way of presenting the radial turbine performance characteristics is to plot the efficiency versus a normalized velocity parameter called blade speed ratio (BR). The blade speed ratio, U r /C s is defined as: 2π D N tc U r = 60 2 (1) 1 Cs κ p κ c 03 1 p T 03 p This relation can be derived under the assumption of ideal gas and isotropic flow. The efficiency versus blade speed ratio characteristic is important when designing turbochargers. For given turbine inlet operating conditions the rotor diameter D should be chosen so that the turbine operating point lies in the high efficiency region during most of the time of an engine cycle. The relation between the turbine efficiency and BR for steady flow is described by a parabola with peak efficiency at a BR of about 0.7 [2], Figure 1. 10

15 Figure 1 An example of a radial inflow turbine characteristic, total-to-static efficiency versus blade speed ratio for steady flow conditions, [36]. It can be understood that the left part of the efficiency parabola relates to high gas velocities and the right to lower gas velocities. The total-to-static isentropic efficiency is the one often used when describing the on-engine turbine efficiency. The efficiency is originally defined as the quotient of the actual enthalpy drop over the turbine and the enthalpy change of the gas if it is expanded isentropically through the turbine: h h TS = η (2) h03 h04, s By reasons of inaccuracies of the efficiency calculated in this way due to thermal radiation losses and also because of difficulties with fast temperature measurements, the efficiency can instead be calculated as the ratio between utilized power and the largest possible power the turbine can extract: P extr η TS = (3) P isentr Dale and Watson [3] calculated the extracted power for a twin entry radial turbine from instantaneous torque measurements. They used a dynamometer to measure the mean torque and the fluctuating torque was calculated from differentiating the turbocharger speed measurement signal. The resulting expression for the instantaneous turbine efficiency: 11

16 dn tc TQ + J N 2 π load cell tc dt η TS = κ 1 κ 1 P κ P κ m& c p T 1 m& c p T 1 exh,a 03,a P exh,b 03,b P 03,a 03,b Using a compressor to absorb the turbine load, the extracted power is calculated as the sum of the compressor power and the power to accelerate the turbine shaft [1]: (4) ηts = P compr P + acc η mech P isentr T02 m& c dt 2 air p 2π dn tc T01 J N + 60 rotor tc dt η mech = κ 1 P κ m c T 4 & 1 exh p 03 P 03 (5) To give a value for the instantaneous efficiency calculated by either of the two latter expressions, care must be taken to compensate for the different measurement locations of the different parameters. The instantaneously measured torque is a result of the state of the fluid in the rotor which was at the measuring location upstream of the turbine at an earlier point in time. Calculating the instantaneous isentropic power a phase lag should be applied to the inlet conditions to account for the different pulse transmission phenomena in the volute casing. A mean volute path length can be used to calculate an estimation of this lag. From CFD analysis of the flow through a turbine under steady and unsteady flow, it is possible to calculate the time for an acoustic and convective wave to pass along the turbine volute. From turbine volute entry to the throat the mass flow pulse was concluded to be an acoustic phenomenon and the temperature pulse a convective phenomenon [30]. This confirms the results by [21]. Downstream of the volute throat the propagation of pulses is more complex, a mix of acoustic and convective transmission. Winterbone et al. [32] compared the travel time for the pressure pulse at turbine volute entry to half the way around the circumference of the casing, with the time for the energy contained in the pressure 12

17 pulse to be delivered at the rotor (through the phase lag between the pressure and torque signals). Since the transmission time for the half way distance is much shorter than the time to reach the rotor they deduced that the lag must be caused by the energy transfer from the casing to the rotor. This since no substantial change in wave pattern was seen along the casing. There is no absolute correct way of shifting the upstream measured quantities. Dale and Watson [5] used the propagation time for a sonic wave whereas Baines et al. [35] and Winterbone et al. [32] used the propagation time for the bulk flow. The results seems to be contradictory, Baines et al. on one hand claim that the bulk flow transmission is more important than the pressure wave transmission in determining the pulse flow performance whereas on the other hand, Karamanis et al. and Arcoumanis et al. [37, 38] state that the opposite is valid. Ehrlich et al. performed measurements in an engine test cell on a turbocharged (twin entry) 6- cylinder medium speed diesel engine with focus on understanding the process of energy transport from the cylinder to turbine inlet [21]. They measured the instantaneous total and static pressure using in house constructed probes connected to a high frequency dynamic pressure transducer. The velocity field in the horizontal central plane was measured, using Particle Image Velocimetry (PIV), at chosen crank angles during the engine cycle to characterize the turbine inlet velocity profile during an exhaust valve event. The results indicated that the transport mechanism in the exhaust manifold must be modeled as both a convective and an acoustic propagation Turbocharger quasi-steady performance modeling The 1D model assumes a quasi-steady behavior of the turbine which means that the turbine is expected to behave at any instant in the same way as it would under steady flow at the given instantaneous conditions. Turbocharger performance data is normally measured by the turbocharger manufacturer under steady flow conditions. This data is used by the 1D engine simulation tool to calculate the compressor and turbine power under both steady and unsteady flow conditions. The calculation of compressor power and efficiency is more reliable than on the turbine side, the on-engine conditions for the compressor are more or less the same as for the steady state conditions [20]. The calculated turbine power is not well predicted and must for almost every operating point be adjusted with efficiency and mass flow parameters (so called multipliers ) to match simulated results to measured values. The level of error of the predicted turbine power is especially pronounced in the low speed and load region, where the waste gate is closed. At these operating points the model cannot control the waste gate opening to let a proper amount of flow 13

18 pass through the valve to meet target boost pressure. The efficiency of the turbine may have to be adjusted by as much as 30 % [1, 29] Adequateness of quasi-steady approach Several researchers have presented results from turbocharger flow measurements. Among them are studies from measurements on turbochargers under steady and pulsating flow, for single and twin entry radial turbines with and without guide vanes, [1, 3, 29, 35]. These authors have shown that the turbine power and mass flow rate show large deviations from their steady state characteristics and there are indications that the quasi-steady approach is inadequate. CFD analysis of a radial turbine [30] shows that the instantaneous performance of the rotor at unsteady flow conditions does not vary significantly from that at steady flow conditions. The results indicate that the rotor could be seen as a quasi-steady flow device for power extraction while the volute passage significantly alters the shape of the unsteady mass flow characteristics. This conclusion is also supported by the results of [35]. Capobianco and Marelli [17, 18,19] performed measurements on a single entry radial turbine in steady and unsteady flow conditions. The instantaneous mass flow rate was measured with a hot wire probe but it was also calculated from the instantaneously measured pressure together with turbine steady mass flow characteristics using the quasi-steady assumption. The amplitude of the experimental mass flow rate oscillations showed to increase substantially with higher average turbine expansion ratio (higher oscillation frequency). This was not seen for the mass flow rate calculated with the quasi-steady assumption where the oscillation amplitude remained almost constant. They suggested that for lower pulse frequencies, if the mass flow rate cannot be measured instantaneously, using that from 1D quasi-steady calculation is quite accurate for turbine efficiency calculations even though other authors as Szymko et al. [41] have highlighted large discrepancies between instantaneous unsteady mass flow rate from quasi-steady calculations and measured values at higher pulse frequencies Performance data A common opinion is that turbine performance data provided by the turbocharger manufacturers is not well suited for research purposes [3]. Baines et al. [4] address the inaccuracies in turbine efficiency calculations to the use of steady-flow turbine data to predict the performance of turbocharged engines, which is also consistent with general experience. Performance data from turbocharger manufacturers, used as input in the engine model to describe the steady flow 14

19 characteristics of the particular turbine, are quite sparse for the open waste gate region, if at all included. Capobianco et al. [17] extended their study to include measurements for a range of wastegate valve opening angles for a single entry nozzle-less waste-gated turbocharger. A compressor was used as a dynamometer and the turbine load range was considerably extended compared to performance data from the turbocharger manufacturer since the tests included the open waste gate region. The gas temperature was about 400 K. The study showed that for a small automotive turbocharger where the flow through the by-pass valve is substantial, maybe even greater compared to the flow that passes the rotor, the flow interactions in the turbine volute casing significantly affected the mass flow rate and efficiency. The overall turbine efficiency calculated from isentropic expansion of the entire mass flow (rotor plus by-pass flow) was much smaller when the waste gate valve was opened while keeping the overall turbine expansion ratio and inlet temperature constant. For small valve openings there was a significant reduction of specific turbine work, probably caused by flow perturbations due to fluid interactions in the dividing section of the turbine housing Turbine behavior under steady and unsteady flow Dale and Watson [3] built a turbocharger test facility in the middle of 1980 to study the turbine's behavior under more engine-like conditions. A dynamometer was used to absorb the turbine load instead of using a matching turbo compressor, or less likely several compressors, which gave a broader load range of the turbine compared to that provided by the manufacturer. The tests were performed on a twin-entry vaneless radial flow turbine in steady and pulsating flow, by the use of counter-rotating chopper valves. To analyze the performance of a turbine under unsteady flow conditions it is most common to use a pulse generator upstream of the turbine. The shape and amplitude using a pulse generator is often different from the situation on a SI engine, [1]. In addition, the heavily fluctuating temperature typical for the on-engine turbocharger is not taken into account. Dale and Watson s work was focused on the aerodynamic efficiency of the turbine so the gas temperature was kept rather low, about 400 K, to minimize heat transfer losses. Prior to their work, studies on radial flow turbines had only included instantaneous measurements of pressure. Dale and Watson also measured the instantaneous mass flow rate and turbine torque. The instantaneous mass flow rate which showed to deviate from the steady flow curve, for a specific speed and turbine expansion ratio, was used in the calculations of the instantaneous turbine efficiency. The results indicated that the turbine did not obey the quasi-steady assumption; the 15

20 unsteady turbine efficiency did not follow the parabolic shaped steady flow curve when plotted against BR, Figure 2. Figure 2 Instantaneous unsteady turbine efficiency versus blade speed ratio for a twin entry scroll turbine (identical inlet conditions) together with the turbine efficiency calculated from the quasi-steady assumption [3]. Instantaneous deviations from the steady flow turbine performance were as high as 10 %. The peak efficiency and mass flow parameter values were higher for the unsteady flow. The cycle averaged turbine efficiency however was lower for the unsteady flow. Baines et al. [4] came to the same conclusion that the instantaneous unsteady flow turbine efficiency was lower than the steady flow value for most of the time during an engine cycle. They considered the deviations from the steady flow behavior to be a cause of flow processes occurring upstream of the rotor. They commented on the instantaneously much higher unsteady flow turbine efficiency, compared to steady-state values, as being misleading since the turbine only spent a short time of the pulse cycle at the high efficiency conditions. The same test rig and performance data acquisition system was used as in [3]. Iwasaki et al. [20] performed steady and unsteady flow measurements on a twin entry turbocharger of a 6-cylinder medium duty diesel engine. They showed that for a fixed turbocharger speed and expansion ratio the unsteady mass flow parameter was lower than corresponding steady flow value 16

21 over the entire operating range tested. The discrepancy was higher for lower expansion ratios, almost 20 %. Karamanis et al. [37] did measurements on a single entry nozzleless radial turbine under steady and unsteady flow. A compressor was used as load absorber. Two counter rotating chopper plates were used to produce the pulsating flow. Their results confirmed the instantaneous deviations between the steady and unsteady performance characteristics. The unsteady cycle averaged efficiency was shown to be lower compared to the steady flow value. Palfreyman et al. [39] compared results from CFD analysis of a mixed flow turbine with experimental data from steady and pulsating flow measurements. The experimental setup and data acquisition system used was the same as [37]. Capobianco and Marelli [19] presented results from measurements on a single entry nozzleless waste-gated turbocharger for a downsized engine, both in steady and unsteady flow with closed waste gate. Instantaneous turbine inlet and outlet pressure was measured with high frequency strain gauge transducers and only averaged values of mass flow rate and temperature were measured. The instantaneous mass flow rate was in the first studies taken from 1D engine simulations whereas later work included measured values from using hot wire probes. Instantaneous temperature was approximated from measured instantaneous pressure and average values of temperature and pressure assuming an adiabatic process of an ideal gas: T 3i = T 3,m κ 1 p 3, i κ p 3, m (6) This approach has been used by many researchers for the instantaneous turbine inlet temperature when only average temperature is measured. Another approach is to assume that the turbine inlet total temperature is constant during a pulse. Then the average temperature can be used to calculate the instantaneous temperature. Using the first approximation, (6), to calculate the instantaneous exhaust gas energy yields good agreement with measurements [37]. Capobianco and Marelli [19] used different approaches to assess the unsteady overall cycle averaged turbine efficiency. Comparing the results from the different approaches they concluded that the most reliable way to determine it was to use instantaneous values for the measured parameters at the turbine inlet and 17

22 outlet. In accordance with the results presented by Dales and Watson [3] and Baines et al. [4] Capobianco and Marelli [19] showed that the steady flow turbine efficiencies (averaged values) were always higher than corresponding unsteady flow values at the same expansion ratio, about 12-13%. No significant differences for the average efficiency levels were found using measured or calculated values. Several studies have shown the presence of clear discrepancies between the steady and unsteady flow performance of the turbocharger. However, to draw the correct conclusions about the turbine behavior from calculated performance parameters it is important to have a good estimate of the accuracy of the data. Baines et al. [4] pointed out that the accuracy in the speed measurement was crucial for correct determination of the instantaneous turbine torque. Dale and Watson [3, 5] also showed that amended measurement of especially instantaneous turbine torque could improve the accuracy of the estimated efficiency significantly. Not only studies on the efficiency are of importance, but also the flow unsteadiness effects on the turbine inlet energy. Results regarding the energy content of a pulse, being higher for pulsating flow than for steady flow, were presented already in the seventies. For a given mean mass flow the turbine produces higher torque under unsteady flow [31]. Capobianco and Marelli [19] presented results from a study on the relation between flow unsteadiness and available energy at turbine inlet. They came to the conclusion that the available turbine inlet energy is a result of both pressure amplitude and mean pressure. Only a little effect was seen for the oscillating temperature amplitude on the turbine inlet energy (for moderate mean inlet temperature). This indicates that the instantaneous temperature approximation from measured instantaneous pressure and average temperature, when instantaneous temperatures have not been measured, can be used in performance calculations without bigger inaccuracies [18, 19] Assessment of flow unsteadiness To get a rough estimation of the deviations for the actual turbine performance from its measured steady flow behavior, one has to determine flow unsteadiness effects. One has to define a measure that characterizes flow unsteadiness in a relevant manner. Work has been done trying to find correlation criteria between steady and unsteady flow. Pulsating flow characteristics are often associated with the ratio between pressure amplitude and its mean value. Iwasaki et al [20] performed steady and unsteady flow measurements in test rig on a twin entry turbocharger for 18

23 medium duty diesel engine application. They showed that a pulsation factor K p for several turbocharger specifications, showed the same trend with turbine expansion ratio. K p is defined as the ratio between the difference in maximum and minimum instantaneous pressure of the pulse and the mean relative pressure at turbine inlet: K p = P Δp 3, m 3, i P atm (7) The pulsation factor was high at low turbine expansion ratios (a value of about 2) and decreased with higher expansion ratios as the flow condition approached that of steady flow. The expansion ratio was calculated with the mean values for turbine inlet and outlet pressure over the pulse. Iwasaki et al. [20] also showed results from measuring the static pressure along the turbine scroll and calculations of the instantaneous flow angle relative to the turbine rotor, the incidence angle β, in steady and unsteady flow. The static pressure variation along the scroll was smaller for low engine speeds. The results indicated that these pressure variations had a greater impact on β which showed larger variations compared to higher engine speed operating points. The variation of β was higher for unsteady flow compared to steady flow at the same turbine speed and BR. Other experiments on a twin entry turbocharger under unsteady flow showed large variations in incidence angle and unfavorable gas angles to the rotor during the pulse, even close to the design point operation of the turbocharger [34]. The relative flow angle effects the incidence losses and thereby the turbine efficiency [20, 32]. In addition Iwasaki et al. [20] showed that the degree of reaction fluctuated along the scroll and differed more from corresponding steady state value at low engine speed. The higher flow unsteadiness was considered to be the cause of it although they could not give any clear explanation. To investigate the deviations of the measured unsteady efficiency from measured steady state values, two correction factors were introduced and used to multiply the steady flow mass and efficiency performance in an iteratively manner until the calculated turbine power was close to the on-engine measured unsteady results. This was made for 4- and 6-cylinder diesel and gasoline engines with single and twin entry turbines at full load conditions. Changing the engine speed and thereby the turbine expansion ratio revealed the same tendency for the two correction coefficients for all tested engines. At higher expansion ratios their values were approximately unity corresponding to steady flow [20]. 19

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25 3. Theoretical background In this chapter the governing equations of fluid dynamics are described. In the first section in a more general sense and in the proceeding sections 1D modeling and in particular engine modeling will be described in more detail, continuing with CFD modeling and then integrated engine/cfd calculations.. The computer softwares used are a commercial 1D engine simulation software, GT- Power, and a CFD software STAR-CD. The same conditions are used to handle the heat transfer modeling in the two codes. However, as heat transfer issues have not been a part of this work, the heat transfer modeling in the two codes is not described further. The last section contains a description of the experimental method Governing equations The governing equations for fluid motion are derived from the principles of conservation of mass, momentum and energy. In general terms for 3D unsteady compressible flow: Continuity equation: ρ + t x j ( ρ u ) = 0 j (8) Momentum equation: t x ij ( ρ ui ) + ( ρ ui u j ) = + ρ f i j Π x j (9) Π = δ p + τ (10) ij ij ij τ ij = μ s 2 u μ δ k 2 ij ij (11) 3 xk 1 u u i j s = ij + (12) 2 x j xi τ ij u = μ x i j u + x i j 2 3 u x k k δij (13) Energy conservation: 21

26 t x j [ ρ h] + [ ρ u j h] = + ( u j p) + ( u j τ ij ) + Q & +W& ext j p t x j q x j x j (14) T q = kt (15) x j In the equations above Einstein summation convention is used. The physical properties of the fluid are assumed to be represented by linear constitutive relations and the coefficient of viscosity (υ) and heat conductivity (k t ). To close the system of equations a relation between the thermodynamic variables ( p, ρ,t, e) is needed. For a perfect gas: p = ρrt (16) The coefficients of viscosity and thermal conductivity can be related to the thermodynamic quantities using kinetic theory, for example the Sutherland s formulas: 3 2 T μ = C1 (17) T +C T k = C3 (18) T +C where C 1, C 2, C 3 and C 4 are constants for a specific gas D modeling The one-dimensional flow model involves the simultaneous of the flow in a pipe-like configuration (Figure 3). The axial velocity component is assumed to be much larger than the velocity components in the cross-.sectional plane. The governing equations are the same for this case as for the general 3-D case. However, by assuming that the flow varies only in the axial (stream wise) direction, the three conservation relations (of mass, momentum and energy) can be simplified. ρ + t x ( ρ u ) = 0 x (19) 22

27 ( ) ( ) x u μ + x dp = u ρ x +u u ρ t x x x x (20) [ ] [ ] ext x x xx x x W Q + x q x u τ x p u t p = h u ρ x + h ρ t & & (21) ρ p = e+ h (22) Consider a straight pipe with radius R, Figure 3. Figure 3 A straight pipe with constant cross-sectional area with a small fluid element representing a control volume, after [40]. One may derive these equations by consider directly the flow in the pipe, looking on the conservation of mass, momentum and energy in a small segment of the pipe (i.e. a control volume) For steady flow of a compressible fluid flowing through a circular constant cross sectional area pipe, Equations (19-21) applied to a control volume of a small element after integration yields: u = ρ u ρ (23) dx f ρu D + + ρu p + ρu p = (24) q u + = h u + h (25) The sub scripts 1 and 2 represent the upstream and downstream conditions of the control volume, respectively, and u is the mean axial velocity, D the pipe diameter and f is the friction factor. 23

28 The friction factor f is used to account for the geometry of the pipe, surface roughness, and Re effects. It may be evaluated for given conditions by the use of various empirical or to less extent through theoretical assumptions and considerations 3.3. Engine simulation The flow and combustion in an internal combustion engine is quite intricate and complicated. Despite this complexity it is conceivable to look upon the engine as a piping system through which the fluid flows, from upstream the inlet air filter to the exhaust pipe, joining engine components as the compressor, the intercooler, the cylinders, and the turbine. Such a simplified approach has the advantage of enabling one to assess different designs in a short time. The main disadvantage of the approach is its limited accuracy and the results are more of qualitative character. However, the applicability of the approach and the errors associated with it are not uniform to all engine components. As shown here, rather good results may be obtained for certain parts of the engine manifolds and less good results for other components such as the turbo-charger or the flow and combustion in the cylinder (not studied here) Model structure To simulate the entire engine the system is broken up into different components as pipes, pipe bends, flow splits and other components as the engine cylinders, the cylinder valves, the compressor and turbine. The flow through the pipe components is modeled with the assumption of one dimensional flow while the flow properties through the more complex parts of the engine as the intake and exhaust valves, the flow through the compressor and turbine, and the combustion process in the cylinder, are modeled without spatial resolution and rely on empirical relations and measured input data. Input data can be measured pressure loss coefficients for the valve flow, crank angle resolved pressure for the in-cylinder process and turbocharger performance maps for the turbine/compressor sub models. More details on the modeling of various engine components are given in the subsequent sections Modeling of fluid flow The equations used to simulate the flow in the different components are the somewhat modified 1D equations (19-22). In the corresponding momentum equation an additional pressure loss coefficient term C p is added to account for bent pipes or pipes with irregular cross sections. The 24

29 pure 1D flow assumption would not capture the effects on the flow that these geometrical properties may cause. The fundamental equations using the explicit time solver and for constant cross sectional area pipes are given by: Continuity: Momentum: d dt ( V ) = ( ρ ρ u A) (26) boundaries d dt dp d ρ u d ρu f ( ρ u) = + ( ρ u u) 4 C p dx dx boundaries D 2 dx 2 C 2 2 (27) Energy: d dt dv [ ρ ( e+u )] = p + ( ρ u A h) hg Atot ( T Twall 2 ) dt (28) boundaries Discretization method The pipe volumes to be modeled are further discretized by the 1D code into smaller sub-segments (control volumes) with a recommended length of typically mm, whereas the flow splits are not further discretized. The method used to discretize the pipe volumes in space is the staggered grid, the scalar variables are solved at locations offset to where the vector variables are solved. Scalar variables as density, internal energy, pressure and temperature are assumed to be uniform over each sub-volume and are calculated at the centre. Vector variables as the gas velocity and mass flux are calculated at the boundaries which connect the sub-volumes. For integration in time can be either implicit or explicit. The explicit time solver is recommended and it is a non-iterative method, for which the time-step size is limited by the Courant condition, dt dx ( u + c) C (29) 25

30 where C is a parameter, less than or equal to 1 and it is set by the user. Using the explicit time step scheme the variables at a new time step is calculated from the variables of the previous time step in the sub volume in question and its closest neighbors. The implicit method uses a set of algebraic equations to solve simultaneously for the values of all sub volumes and boundaries at the new time step in an iteratively manner until convergence is reached. The explicit method will more accurately predict pressure pulsations that are important in engine systems Pipe flow Pipe objects are used to model the flow through tubes with constant or tapered diameter and the code assumes uniformity of the flow field in the perpendicular planes. The code assumes circular cross-sectional area but the user can adjust heat transfer multipliers, friction multipliers, and /or pressure loss coefficients to account for affects of other geometries Straight pipe Flow losses due to wall friction is calculated using expressions for the skin friction coefficient C f as a function of Re and wall roughness. For turbulent flow, Re>4000 and for a smooth pipe: 0.08 C f = (30) 0.25 Re For a rough pipe this parameter has a larger value than given by equations (30) and hence equation (31) is used: 0.25 C f, rough = (31) 2 1 D 2log hr Re is based on the pipe diameter. If necessary a friction multiplier can be used to scale the calculated friction in a single pipe or flow split and it is also possible to use a global steady friction multiplier comprising all pipes. For increased frictional losses due to unsteady flow, like the pulsating flow of an engine, a global unsteady friction multiplier is used. It scales the calculated friction losses in all pipes and flow splits and is adapted to the amplitude and frequency of the pulsatile flow. 26

31 C f = C f,s const ( + M F ) M 1 (32) unst unst C f is the instantaneous friction factor, C f,s the instantaneous friction factor using correlation for steady flow, M const is the constant global friction multiplier (set to 1 for unsteady flow), M unst a global unsteady friction multiplier, and F unst is the instantaneous unsteady friction factor. The latter is calculated by the code at every time step but is a hidden function for the user. It depends on the fluid viscosity and acceleration among other quantities. Gamma Technologies comment on the unsteady friction modeling to be experimental and only to be validated for a limited set of measurements from data for liquid systems Bent pipe Pressure loss coefficients are used in the code to account for pressure losses in pipes due to the effect of irregular cross-sections, decreasing pipe diameter or bends. The pressure loss coefficient C p can either be calculated by the code or be set by the user. It is defined as the dimensionless pressure loss: C p = ( p p ) tot,1 1 ρ 2 1 u tot,2 2 1 (33) where subscripts 1 and 2 denote the upstream and downstream conditions of the bend, respectively. The exact calculations of the forward and reverse pressure loss coefficient are unknown for the user, but they do not include the wall friction Flow split When a sub volume has several openings it is defined as a flow split. The methods used for the flow through a flow split are very much as that of a pipe. The scalar quantities as mass and energy are solved at the centre of the volume but the flow split is designed to conserve the momentum in three dimensions and the momentum equations are solved separately for each of the volume openings. A characteristic velocity vector is calculated from all of the ports of the flow split and the outlet momentum flux is calculated by using the component of the characteristic velocity in the direction of the outlet port [42]. 27

32 3.3.3 Engine cylinder The intake and exhaust ports of an engine cylinder are modeled as pipes even though special considerations must be made to model the friction and heat transfer losses correctly. The modeling of cylinder valves requires measured discharge coefficients to properly describe the flow area and the in-cylinder combustion process needs input from measured cylinder pressure to determine the energy released at every crank angle Combustion model The role of a combustion model is to simulate the amount of energy generated during combustion. The first law of thermodynamics states that energy released by combustion of the fuel (δq) equals the heat transfer to cylinder walls (δq HT ), energy lost into the crevices (δq Crev ), the change in internal energy (δu) and the amount of work done by the system (δw): Q = Q + Q + U + W (34) HT Crev The rate of heat release can then be expressed as: Q = θ p V Q + HT QCrev f p, V,, + (35) θ θ θ θ The measured cylinder pressure, if measured, can be used as input to calculate the overall heat release rate over an engine cycle Engine cylinder valves Different types of cylinder valves can be modeled with the use of object templates for the characteristic valve in question, a cam driven valve for instance. The valve is seen as a special type of connection. Connections are planes joining physical components together, locations at which the momentum equation is solved to compute the mass flow rate and velocity. Valve connection objects require input of a discharge coefficient describing the flow area. This is to correct for frictional losses and errors in the assumption of the velocity profile. It is needed for both directions of the flow through the valve and it is given for varying valve lifts. The discharge coefficient C D is defined as the effective flow area divided by the reference flow area (on which the measurements are based on) and it is usually calculated from flow measurements on the cylinder head. For gases: 28

33 m& = A ρ U = C A ρ U (36) eff is is D R is is is ( P ) 1/ γ ρ = ρ (37) 0 R 1 κ U 1 κ is = RT0 PR (38) γ Turbocharger The 1D engine model comprises a turbine sub-model which is simulated by a zero-dimensional object in space. The turbocharger is replaced by parameters that are based on turbocharger performance data under steady flow conditions in a gas stand using air at moderate temperature Performance maps The turbocharger performance maps contain series of data points describing the different operating conditions of the compressor/turbine by turbo shaft speed, mass flow rate, pressure ratio and efficiency. The maps are preprocessed by the software since the original available data points are often sparse and do not cover the entire operating range of the heavily pulsating mass flow rate and pressure ratio for on-engine turbocharger application. To create suitable maps that define the turbine performance, the raw data is not only interpolated but also extrapolated to give data at the high and low extreme values of engine speed, pressure ratio, efficiency, and mass flow rate. A typical turbocharger efficiency performance map for a gasoline passenger car is shown in Figure 4: 29

34 Figure 4 A turbine map for turbocharger 1, generated by GT-Power. White circles are the measured raw data from the turbocharger manufacturer and the color field the extra- and interpolated map points needed in the simulation. The simulation entry points during an engine cycle at 1300 rpm and wide open throttle are also shown, after [29]. It is quite clear that the actually measured data points are quite few, especially in the low mass flow rate and pressure ratio region Numerical computation of turbulent flows In the following sections we consider the model (conservation) equations and the additional equations needed for accounting for turbulence. Thereafter we consider the needed boundary conditions to solve the system of equations. The following sub-sections deal with numerical issues; namely discretization of space and the differential equation and possible solution algorithms for the resulting system of non-linear algebraic equations. Computational fluid dynamic (CFD) has different meaning depending on the context. In the strict sense it deals with numerically solving a system of partial differential equations related to fluid flow, with appropriate boundary conditions. In a more general sense CFD means solving a scientific or engineering flow problem using computational methods as a tool for obtaining the sought results. In the following we use CFD the latter sense Basic conservation equations The governing equations of fluid motion (equations (8)-(15)) are well established since over 150 years back. These equations have analytical solution only for a small number of cases (geometry 30

35 and parameter values). These partial differential equations are derived from the conservation of mass, momentum and energy. The governing equations in Section 3.1 are written in a general form (Cartesian coordinate s notation) and apply to incompressible and compressible flow whether it is laminar or turbulent. For turbulent flow the dependent variables solved for are the ensemble averaged values, the mean quantities, and an extra term adds to the momentum equation to account for the additional stresses due to the velocity fluctuations about the mean value. This additional stress is linked to the mean velocity field through turbulence models and will be further explained in the following Turbulent flows and their modeling Fluid flow can be characterized as being either laminar or turbulent. A dimensionless parameter, the Reynolds number (Re), is used to characterize flows to the importance of inertia relative the importance of viscousity. Re is defined as: U L Re = (39) υ Thus, Re is a combination of the property of the flow (i.e. characteristic velocity U), the geometry (characteristic length L) and the property of the fluid (the kinematic viscosity υ) Turbulent flows a characterized by large values of Re. How large Re should be in order to have a transition from laminar to turbulent flow is problem dependent. Turbulent flow through a pipe can be described as being composed of a mean flow in the direction of the pipe axis together with random irregular velocity fluctuations in all three directions. This irregular motion, if visualized resembles (random) motion of eddies of different sizes. The term eddies is often used in turbulence without giving an exact definition to it. However, loosely speaking the eddies have a size and thereby they are related to the length scales that are found in a turbulent flow field. All eddies are in random motion relative to each other and the largest have the size of the flow itself. Due to the randomness of the motion a statistical approach must be used to characterize the flow and to be able to analyze and compare different flows (in the same or lookalike geometries). Large scale motions are limited by the geometry of the vessel. The large scales are responsible to the fast long-distance transport and mixing. Smaller scales determine the local mixing. The smallest scales of the flow are determined by the rate at which viscosity can eliminate energy from the smallest eddies. The smaller the eddy (scale) is, the faster it decays (for a given 31

36 kinematic viscosity of the fluid). The smallest scales are thus independent of the flow geometry and the largest scales of the flow. The big separation between the small and large scales of turbulence is the basis of the classical turbulence theory of Kolmogorov. Energy is transferred in average from the larger scales to the smaller ones. Eddies are like stirrers, transporting fast moving fluid from the center towards the wall with low momentum flow. Large-scale stirring by these turbulent eddies together with momentum diffusion down the local velocity gradients give a very effective transport of momentum. For turbulent flow the momentum transfer is estimated to be thousands to million times more effective than for the laminar case in which molecular diffusivity is responsible for the mixing. Better transport of momentum gives higher shear stresses at the wall and greater resistance to the flow. Greater sheer stress at the wall means more drag on vehicles and larger pressure drop in pipes. But higher wall shear stress also comes with positive effects as better mixing and enhanced heat and mass transfer, essential for combustion in the engine cylinder for example. The Navier Stokes equations describe the flow whether it is laminar or turbulent. For high Re flows however, the scale ratio of largest to smallest, is too large to be able to handle on currently available computers. Therefore Direct Numerical Simulation (DNS) can be used to study only relatively low Re turbulent flows. For higher Re, statistical methods describing the turbulent flow in terms of the mean velocity field and higher moments has to be used. The averaging processes of the dependent variables and the governing equations lead to the formation of higher order correlation terms. Describing/modeling these terms in terms of low order statistics is referred to as the closure problem. These additional terms (such as the Reynolds stresses) must be linked (in the simplest cases) to the mean velocity field through turbulence models. In this way the set of equations needed to solve for the properties of the turbulent flow becomes closed in the sense that the number of equations equals to the number of unknowns. For high Re flow the instantaneous velocity varies randomly in both space and time. To solve for the instantaneous velocity would not be feasible. The approach is to perform statistical analysis and use the governing equations to solve for the mean flow properties. One way to do this is called the Reynolds decomposition. The dependent variables are separated into a mean component and a fluctuating component. For the velocity vector this yields: 32

37 ( X,t) U ( X,t) + u ( X,t) U = (40) The instantaneous velocity vector U is the mean value U plus a fluctuating component u. Substituting for all the dependent variables, written as a mean and a fluctuating component, into the Navier Stokes equations, results in the Reynolds Averaged Navier Stokes equations (RANS). This procedure leads to the presence of additional terms in the RANS equations, such as the Reynolds stress tensor in the momentum equations. Most often one uses two additional variables to characterize the local turbulence. The turbulent velocity scale can be easily related to the specific turbulent kinetic energy, k, at least for isotropic turbulence. As a second variable one may use the rate of dissipation of turbulent kinetic energy, k, or some other variable. Most often, these two variables are computed through their own partial differential equation. These equations can be derived from the basic conservation laws with the addition of some assumptions (and models) so the system of equations can be closed (i.e. being solvable). The relation between the stress tensor components τ ij and the velocity gradients in the Navier Stokes equations for the laminar case is given by (13) (for a so called Newtonian fluid). For the turbulent case using RANS the fluctuations about the ensemble averaged velocity gives an additional term, ρ u u, called the Reynolds stress. The expression for the stress tensor becomes: i j U U U i j k τ ij = μ + δij ρ u i u j x j x i 3 xk 2 (41) The Reynolds stresses represents the additional stresses due to the fluctuating components of the turbulent flow and they must be related to the mean velocity field. This is done through the use of turbulence models Eddy Viscosity Models There are several turbulence models available and they are subdivided into different categories. In the classical Eddy Viscosity (k-ε) model the Reynolds stresses are directly related to the local gradients of the mean velocity field through: 33

38 ρ u u i j = υ S T ij 2 U υt 3 x k k + ρ k δ ij (42) U U i j S + ij = (43) x j xi k u i u i = (44) 2 To close the set of equations the turbulent viscosity ν T must be expressed with known quantities. The turbulent viscosity is linked to k and ε by: υ T 2 ρ k = Cμ (45) ε C μ is an empirical coefficient, often set as constant. There are different variant of k ε models which may differ in the form of the equations, the treatment of the near wall region and/or in the relation between the Reynolds stresses and the rates of strain (there are both linear and non-linear relations) Boundary conditions Boundary conditions determine the particular flow field, since the basic governing equations are not problem dependent. One may use different types of boundary conditions, but not all possibilities lead to a solution or a single solution. Thus, only certain combinations of boundary conditions lead to a well posed problem (i.e. a problem which has a unique solution that depends continuously on the boundary data). An example that leads to a not well posed problem is if the total mass to and from the domain is not in balance. Examples to possible boundary conditions are such that defines the inlet mass flux and fluid properties, whereas at the outlet boundaries, the gradients of the variables across the boundary surface are assumed to vanish. It is common that commercial codes require less number of conditions than those required theoretically. This may happen since the code itself includes assumptions not specified by or to the user. Such effects may sometimes lead to difficulties in interpreting the numerical results. 34

39 Turbulent flow boundary conditions Most popular turbulence models are based on partial differential equations. These equations also require appropriate (for well posedness and physically reasonable) boundary conditions on the boundaries of the domain and on solid objects Wall boundary conditions At solid walls no-slip condition (zero velocity) are natural and correct from physical and mathematical point of view. However, in the boundary layer close to the wall there are very large velocity gradient in the wall normal direction. To resolve numerically such large gradients one must have an appropriate resolution. The mean behavior of turbulent flows near solid (straight) walls at very high Reynolds numbers can be described by a model that is physically sound. This description is termed as the law of the wall. The law of the wall describes the velocity profile in the wall boundary layer which is made up of a viscous sub-layer, a buffer zone and a logarithmic layer. This approach eliminates the need to study the details of the flow very close to the wall. Instead the near wall region is replaced by the wall model. It should be pointed out that this model is valid only for fully developed (high Re) turbulent flow past a straight (in the streamwise direction) wall. In a real engine geometry, these requirements are hardly met. However, it is even more difficult to define better models for transitional flows with large scale penetrating and altering the classical form of the boundary layer. In the framework of standard turbulence models (such as the k-ε system) one uses one or another version of the law of the wall or alternatively turbulence models that are acting at different distances from the wall. For the standard wall function the boundary layer is just one grid cell thick with its central node assumed to be at a certain distance from the wall. For example STAR-CD offers two-layer wall models also in addition to the simpler wall functions to represent the distribution of velocity, the turbulence energy, temperature etc. across the boundary layer. With the two-layer models the near wall region is treated more or less like the interior flow with the no-slip condition applied directly to the boundary cell faces. At some distance from the wall though, where the viscous effects are small, the k ε turbulence model is switched to a low Re form of the governing equations. A finer mesh is needed for the near wall layer. 35

40 3.4.4 Inlet conditions Using the RANS equations together with a turbulence model both the inlet mean velocity and certain turbulence quantities are needed. The turbulent kinetic energy k is sometimes available from experiments but otherwise it can be assumed as a portion of the mean flow kinetic energy. It is often much smaller than unity and for fully developed turbulent pipe flow it is of the order 10% or less. The dissipation rate of turbulent kinetic energy ε is difficult to measure and can be estimated by assuming or knowing k and the turbulent integral length scalel. The latter is bounded by the characteristic dimensions of the vessel or the device Discretization The continuous differential equations are valid for all points in the space of interest and for all times. The first step in formulating a tractable problem is to restrict the problem into a finite number of (discrete) points in space and time. This process leads to a set of distinct points in the domain of interest. The functions that we are interested in are defined only on this finite set of points. If the set of points can be organized so that the points become vertices for polyhedral volumes we can talk about local control volumes. The conservation of mass, momentum energy (and turbulence quantities) can be satisfied for each control volume. This approach leads to the so called Finite Volume (FV) approach. If one uses polynomial approximations to the dependent variables one may derive finite difference or finite volume approximations to differential equations. The order of approximation is defined as the exponent of the typical grid (volume) size in the expression of the discretization error. The integration in time is also done through a finite different type of expression; explicit or implicit. In the latter case an iterative approach has to be used so as to ensure the convergence of the iterative process to a prescribed level of error. The integration in time allows one to study both steady-state and transient cases. In the following some details of the methods we have used are given Spatial discretization of the convective term There are different classes of convective flux approximation and the choice of it is especially important at high Re. STAR-CD offers several schemes. One lower first order scheme is the Upwind Differencing scheme (UP), generating discretized equation forms that are easy to solve but has the effect of smearing out gradients (numerical diffusion) and should in general be avoided. Higher order schemes include among others second order Linear Upwind Differencing scheme 36

41 (LUP), Central Differencing scheme (CD) and a Monotone Advection and Reconstruction scheme (MARS). Higher order schemes may better preserve steep gradients but may result in equations that are more difficult to converge and even lead to numerical instabilities and/or introducing nonphysical spatial oscillations Temporal discretization There are two options for the temporal discretization in the used code; either a first order fully implicit scheme or a second order Crank-Nicholson scheme. Using the former scheme the fluxes over the time interval are calculated from the new time-level values of the variables. The latter is second order accurate in time but may generate non-physical oscillations if the time step size is too large. Even though an implicit scheme avoids stability restriction on the time step size compared to explicit schemes, the time step is in practice still limited by other factors, such as the needed temporal resolution to follow transients of the flow. This means that the Courant condition (29) must be satisfied. In particular this may mean that there is a need for small time steps for grids with small mesh spacing or for flow with local high velocity Discretization error estimation In the used code the error estimation gives an approximated magnitude and distribution of the convergence error. In contrast to the convergence error it is much more difficult to assess the discretization error. This error includes the errors caused by the finite mesh spacing, its irregularities and discretization errors of the derivatives in the differential equations. Further error may be due to the time-step taken in the temporal integration of the discrete governing equations. The most difficult error to estimate is the modeling error itself (i.e. the error due to the differential equations themselves). Of course comparison with experiments is a way to assess the global accuracy; however, this approach is very crude since it includes also experimental errors and uncertainties as well as uncertainties in the boundary conditions that are imposed in the numerical calculations. The implemented Residual Error Estimate (REE) method is based on a cell residual from the local imbalance between the face interpolation and the control volume integration. The cell residual of a specific variable is then normalized in a proper way to give an estimation of the absolute magnitude of the convergence error with the same physical dimension as the variable in question. This error 37

42 estimator has limited value as explained in the paragraph above, though it is important to know it as an indicator Solution algorithm STAR-CD use implicit methods to solve the algebraic FV-equations that results from the discretized governing equations. There are three implemented algorithms that can be used: SIMPLE, PISO, and SIMPISO. SIMPLE and SIMPISO are solely for steady state calculations and PISO can be used for both steady state and transient applications. Common for all three algorithms is: A predictor-correction strategy by temporarily decoupling the flow equations from each other so that they can be solved sequentially (operator splitting). The vector set of unknowns are split into a sequence of scalar sets. A combination of the FV mass and momentum conservation equations gives an equation set for the pressure enforcing the continuity. o The solution sequence is a predictor step that produces a tentative velocity field and the preliminary fields are then refined in one or several corrector stages so that the mass and momentum equations are both satisfactory balanced. As the dependent variables are decoupled and also linearized they result in large sets of algebraic equations. The equations resulting in the above mentioned correction steps are often a Poisson equation. That equation can be solved efficiently by either Conjugate-Gradient method or by a Multi-Grid method Coupled 1D & 3D simulation tool The coupled simulation tool that has been used in this work is integrated calculations using the 1D engine simulation software GT-Power and the CFD software STAR-CD. By integrated calculations is meant that through special connections in the 1D model, the 1D code exchanges boundary values to the 3D computational domain at each CFD time step. This allows for a detailed modeling of geometries where the 1D flow assumption is less appropriate, for components with significant 3D flow, and the remainder of the engine system can be modeled in 1D. The computer cost can be 38

43 kept very low as the CFD domain is restricted to parts of the engine where it is mostly needed and not the entire system of components Boundary interfaces The coupling between the two softwares occurs at the boundary interfaces (cell faces) of the connection objects in the 1D code. A sketch of the1d-3d interfacing boundary geometry is shown in Figure 5. Figure 5 A sketch of the 1D-3D interfacing boundary geometry. The figure shows three boundary interfaces which are the locations for the exchange of information between the CFD domain being modeled in STAR-CD and the rest of the 1D geometry being modeled in GT-Power. It is very critical that these boundary interfaces are placed in areas where the flow is almost one-dimensional. The flow entering/leaving the 1D/3D boundary regions must not have too large secondary flow components as this may lead to incompatibility between the two solvers. Additionally, the mismatch may also leas to stability problems with oscillations or even divergence of the coupled system. In fact the coupled system may not have a solution at all as long as the level of incompatibility is significant. Since GT-Power is one-dimensional the three-dimensional CFD results must be averaged over a plane before being passed back into the 1D code interfacing parts. This region is the 2D cross sectional area of the 39

44 individual1d/3d interfaces times a certain length into the CFD domain, marked as the shaded areas extended a length DX into the CFD domain in Figure 5. In this way the interfacing CFD regions can be thought of as sub-volumes adjacent to the GT-Power sub-volumes where DX is set to the discretization length in the 1D code. The CFD code controls the starting and ending of the 1D calculations. The latter is first run for a number of cycles (time steps) alone to give better boundary conditions sent into the CFD model when the coupled calculations start, i.e. without start up transients. There is also a way to prepare the 1D model in order to produce not only good boundary conditions but also good initial conditions. GT-Power then has to be run in its original state and data as temperature, pressure and velocity for the pipe object next to the CFD domain is stored and later used in the coupled simulation to initialize the flow field in the CFD model Time stepping The time steps used by the codes are typically not equal as the CFD code is often run with an implicit discretization scheme and GT-Power an explicit scheme with adaptive time stepping based on the Courant condition. Usually the time step size used by GT-Power is smaller than the CFD code time step. This means that GT-Power will step a number of times until completing a full CFD time step so that the two codes at the end of the CFD time step are at the same point in time Experimental method Engine in test cell The experimental tests are performed on a 4 cylinder 2-liter standard production turbocharged SI engine from For measurement and control, a PC based in house system is used Measurement methods The measurement system takes both analogue and digital input. Analogue input is measured by using either a fast system for crank angle resolved data or by using a slower time averaged system. The fast system consists of a 12-bit PowerDAQ card [6] with a sampling frequency of 1.2 MHz divided over a maximum of 16 channels. The resolution used in this work is 0.4 CAD corresponding to a total sampling frequency of approximately 0.23 MHz at 1300 rpm. The slow 40

45 measurement system has a sampling frequency of 1 Hz and it is built up of different Nudam modules [7] for analogue voltage input or thermocouples output signals Pressure The cylinder pressure is measured on all cylinders with GM12D cylinder pressure transducers [8]. The pressure is measured at several locations on the engine: before and after the compressor, in the inlet and exhaust port of cylinder 4, in the inlet plenum, and just upstream and downstream of the turbine. The fast analogue system is used for the pressure measurements, on the intake side with strain gauge transducers and on the exhaust side with piezo-resistive transducers Temperature Measurement of the mass averaged temperature at different locations on the engine uses the slow analogue system. Thermocouples are mounted before and after the compressor, after the intercooler, in the inlet plenum, before and after the turbine and in the catalyst Mass flow rate The exhaust gas flow is measured indirectly by measuring the fuel flow and the air to fuel ratio (AFR). It was compared with results from the control system measurement of the inlet air mass flow rate and lambda measurements Turbocharger speed When modeling a turbocharged engine it is most important to get the turbocharger speed correct. A Micro-Epsilon eddy current probe [9] is positioned on the compressor shroud. The transducer senses the blade passages of the impeller and a signal processing unit converts this output signal, in this case, to one digital signal per revolution. At a turbo speed of rpm and an engine speed of 1300 rpm, the turbine speed is determined every 5 crank angle (from the time between two consecutive pulses). The turbo speed is then linearly interpolated to instantaneous values at the crank angles for the analogue measuring points. The digital system used for the turbine speed measurement consists of a Microchip PIC18F452 microcontroller recording the pulse time with a time resolution of 10-7 s. The time data are continuously transferred to the PC and synchronized with the analogue system. This is done by measuring the one per engine revolution pulse with the same 10-7 s time base for each revolution during the measurements. 41

46 42

47 4. Results The first part of this chapter shows the results from calibration of a 1D engine model to measured data. Results are then presented for a study where the calculated instantaneous turbine efficiency from 1D engine simulation using steady flow turbine performance maps is compared with the turbine efficiency calculated from on-engine measurements. Two different turbochargers are considered. Results are also presented for a comparative study between 1D and CFD calculations on single and double bent pipe geometries under steady and pulsatile flow. Results related to the comparison between the 1D and CFD calculations on the exhaust manifold are shown. Initial results of the integrated 1D and CFD calculations are summarized Engine modeling Modeling the engine as a system of zero and one dimensional components implies that data is needed as input to the models to give accurate results. Trends for various engine output performance parameters can easily be seen when varying different parameters in the engine model. However, the 1D engine calculation tools suffer from limited predictivity of turbocharged engine models. Measurements as turbocharger speed, air mass flow rate, and cylinder pressure are needed for thorough model calibration [1, 29, 36]. One source of error is the treatment of the turbine as a quasi-steady flow device and probably also the simulated inlet conditions used for interpolation in the performance maps since the geometry upstream of the turbine contains secondary flow structures Calibration The model is calibrated by controlling the cycle averaged turbo speed to measured values. The calculated turbine power is not well predicted and must often be adjusted with efficiency and mass multipliers to give simulated results close to measured values. Problem with erroneous predicted turbine power is especially pronounced in the region where the waste gate is closed since the model cannot control the waste gate to meet target boost pressure. For this purpose, and with closed waste gate, a PI controller controlling the turbine efficiency multiplier is used in the model. Adjustments are then made to other parts of the model to get important variables close to measured, volumetric efficiency among others. The compressor model needed no correction. A comparison between measured and simulated pressure traces before and after the turbine as well as turbo shaft speed and shaft acceleration are shown in Figure 6. 43

48 Figure 6 Measured and simulated pressure traces before and after the turbine (P1T, P2T), turbo shaft speed (Ntc) and shaft acceleration (dntc/dt) for TB1at 1300 rpm and wide open throttle. After calibration measured and simulated results show good agreement. The relative error is 1.5% and 3%, respectively for the cycle averaged pressure before and after the turbine for TB1 and TB2 it is 1.6% and 0.4%, respectively. The relative error for the cycle averaged inlet temperature and mass flow rate are 0.2% and 0.9% for TB1 and 0.2% and 2.6% for TB2 at 1300 rpm Instantaneous turbine efficiency A comparison is made between the calculated instantaneous turbine efficiency from 1D engine simulation using the quasi-steady flow assumption and that from on-engine measurements. High frequency measurements are required to calculate the instantaneous turbine efficiency over an engine cycle according to equation (5). However, since high resolution mass flow rate and 44

49 temperature measurements are difficult to perform in on-engine applications, only cycle averaged quantities are measured. The instantaneous values for mass flow rate and temperature used in the efficiency calculations are therefore taken from engine simulations and require well calibrated models. Crank angle resolved measurements as pressure and turbocharger speed are averaged over 300 consecutive cycles. The on-engine turbine efficiency is derived for two different turbochargers, TB1 and TB2, in the closed waste gate region with the engine running at 1000 and 1300 rpm and wide open throttle. Figure 4 shows that the operating point during an engine cycle for TB1 at 1300 rpm is in the extrapolated region of the generated turbine map during large periods. In Figure 7 the TB1 turbine efficiency is shown versus blade speed ratio (BR) as is common when presenting turbine efficiency characteristics. For simplicity the results are presented for only one of the four exhaust pulses, as they all show the same behavior. Figure 7 Comparison between instantaneous turbine efficiency based on measurements and results from using tabulated steady-flow efficiencies versus U/Cs, for TB1 at 1300 rpm and wide open throttle. The additional markers show the points of the pulse exceeding 2 kw. 45

50 The arrows in Figure 7 show how the efficiency is changing as one exhaust pulse is traversed through the turbine. The highly fluctuating mass flow, pressure, and isentropic power at turbine inlet all peak near the region of the lowest blade speed ratio point, the left most point in Figure 7. The same efficiency characteristic as for TB1 at 1300 rpm is seen for TB2 and also for the 1000 rpm cases, as shown in Figure 8. Figure 8 A comparison between the instantaneous turbine efficiency, based on measurements and results from using tabulated steady-flow efficiencies, versus U/Cs. The upper diagram shows TB2 at 1300 rpm, the lower left diagram TB1 at 1000 rpm and the lower right diagram TB2 at 1000 rpm, all at wide open throttle. The markers show the points exceeding 2 kw. The measured efficiency shows somewhat similar results for the two turbochargers. At 1300 rpm, the instantaneous efficiency for TB1 and TB2 increases on the upslope of the pressure pulse to a maximum value of about 0.65 before the mass flow and pressure pulse peak. The efficiency decreases to approximately 0.5 at pulse peak (lowest BSR point) and then again it increases, on the down slope of the pulse, to about 0.9 (higher for TB2 though). Similar results for the measured efficiency of TB1 and TB2 also holds for the 1000 rpm cases. 46

51 Ignoring the lowest energy points of the pulse, the results show that measured instantaneous turbine efficiency compared to tabulated steady-flow efficiency values agree better on the upslope part of each pressure pulse from close to the maximum efficiency region and up to the peak of the pulse, Figure 8. The point of peak pressure coincides more or less with maximum energy and mass flow rate into the turbine. From this point through and continuing on the downhill side, the measured efficiency starts to differ to a greater extent and has a value well above the efficiency from steady-flow performance maps. The turbine efficiency characteristic derived from measurements and that from using steady-flow efficiency performance maps, describe quite different behavior of the turbine. The provided steady flow efficiency data for TB1 and TB2 differs quite a lot when looking at the maximum efficiency level. Sensitivity to measurement installation might be a cause of it. Even though measured efficiency for turbocharger 1 shows better agreement with tabulated steady flow data than turbocharger 2 does, it is clear that the on-engine instantaneous efficiency, for both turbochargers and load points, is significantly higher on the downhill side of each exhaust pulse. The measured turbine efficiency shows a hysteretic effect with an unrealistically high efficiency for decreasing mass flow rate after pulse peak. To investigate if the region of high measured instantaneous efficiency (not considering the lower energy part of the pulse) will have any affect on the cycle averaged efficiency compared to results obtained using efficiency performance maps, the time spent by the turbocharger in this region of the exhaust pulse is important. For TB1 at 1300 rpm the efficiency is plotted against crank angle instead of blade speed ratio, Figure 9. 47

52 Figure 9 Comparison between instantaneous turbine efficiency based on measurements and results from using tabulated steady-flow efficiencies versus crank angle. The figure includes isentropic power at turbine inlet and markers on the efficiency curves showing the points exceeding 2 kw.(top figure, a). BR versus CAD. Both figures are for TB1 at 1300 rpm and wide open throttle (lower figure, b). Figure 9 shows the efficiency together with turbine inlet isentropic power versus crank angle for TB1 at 1300 rpm. The figure also shows how the blade speed ratio varies during the same crank angle interval. According to Figure 9 the crank angle interval of the pulse indicating large discrepancy between measured and quasi steady flow efficiency can be expected to be important as the energy is still at moderate levels (region of decreasing mass flow rate following upon pulse peak). It will have an effect on the time and mass averaged efficiency during an engine cycle and the importance it may have on turbocharger matching Accuracy of the calculated turbine efficiency Results related to the effect of different measurement errors on the calculated efficiency are presented in this section. Only steady-state errors are considered for the individual measurement errors, they do not include inaccuracies due to the pulsating conditions. For simulated parameters as temperature and mass flow rate, errors from differences in measured and simulated cycle averaged values are added to the instrumentation error. 48

53 The variables in eqn. 5 are all marred by measurement errors. The uncertainty in the calculated turbine efficiency depends on these individual measurement errors. The variance for the calculated total-to-static turbine efficiency σ 2 can be estimated with the use of Gauss approximation η TS formulas, describing the laws for error propagation of non-linear measurement equations [10].Using Gauss approximation formula gives the expression for the variance of the turbine totalto-static efficiency: σ 2 η TS = i=n i= 1 η x TS i 2 σ 2 x i (46) where σ 2 xi is the variance for the measured parameter x i. The instantaneous total-to-static efficiency as a function of the individual independent variables (4): η TS = f ( X ) = f ( J rotor, N tc,mair,t01,t02,t03,t04,m& exh, P03, P4 & ) (47) Figure 10 shows the instantaneous efficiency together with its crank angle resolved variance during one exhaust pulse. The individual measurement error contributions to the efficiency variance are also shown. Figure 10 Turbine efficiency, efficiency variance and the different individual measurement error contributions. TB1 at 1300 rpm and wide open throttle. 49

54 It is clear that the accuracy of the measured efficiency is mainly determined by the measurement error of the turbine shaft speed. The pressure before and after the turbine are also important. The efficiency variance goes to infinity as the energy of the pulse vanishes. The sensitivity of all the other measured parameters is very low. It must be pointed out that the dynamic errors are not accounted for and also the sensitivity of the phasing of different parameters in equation (5) is not considered, for example the phase shift between mass flow rate and shaft power. The pressure trace after the turbine was difficult to simulate correctly and according to Figure 6 in the calibration section, there are some discrepancy in the upward peaks between measurement and simulation. This can affect the instantaneous mass flow rate used in the efficiency calculations since they are simulated averaged values between the exhaust gases flowing into and out of the turbine at each instant. If the pressure trace after the turbine suffers from difference in phase between measurement and simulation, it is possible the instantaneous mass flow rate will do that as well. Phasing of the mass flow rate was shown to be very critical when calculating the efficiency using equation (5) CFD modeling of pipe flows The primary purpose for introducing the CFD modeling was to integrate full CFD calculations on the exhaust manifold of a turbocharged SI engine passenger car with 1D engine calculations on the rest of the engine. The question at issue was if the inlet conditions to the turbine would be affected by taking the multidimensional flow effects in the upstream exhaust manifold into account in the 1D model. However, the operating points considered where such that problems as reverse flow at the outlet of the CFD-domain made this task difficult to realize due to the limitations in applying appropriate boundary conditions in the commercial code. This was even true for the case with extension volumes added at both the inlet and outlet end of the domain. As stated above, it is not self evident that the coupled system can have a solution for small but finite incompatibility between the 1D and 3D models. Thus, the attempt of extending the domain may not be adequate to prevent oscillations or divergence of the process due to the instability of the interfacing at the 1D/CFD boundaries. The focus was instead on comparing the results between 1D and CFD analysis of the exhaust manifold, both under steady-state and pulsating flow conditions. For the pulsatile flow case the flow showed a considerable separation bubble after the strong bend just upstream of the end of the computational domain (i.e. the outlet boundary). In addition, it was difficult to draw direct 50

55 conclusions from the different results as the effects of the error introduced by creating a 1D model from the 3D manifold geometry was difficult to estimate. Thus, in order to gain a better understanding of the different problems, a set of simpler cases have been studied. These geometries have been used to assess the effects of the 1D assumption and the discrepancy between the 1D and 3D results in terms of losses Methods For the different geometries modeled in STAR-CD the equations of fluid motion has been solved using the Reynolds Averaged Navier Stokes equations (RANS) together with a κ ε RNG turbulence model. A second-order MARS scheme was used for spatial discretization and a full implicit first order scheme was used for temporal discretization. For the steady state problems the SIMPLE solution algorithm has been used to solve the final discretized FV equations and for the transient problems the PISO algorithm. From the decoupling of the equation for each dependent variable and their linearization, the resulting large sets of linear algebraic equations are solved with an algebraic multigrid approach (AMG). A numerical accuracy study performed by Hellström on a single and double bent pipe [28] showed that the order of accuracy of the STAR-CD code is between 1 and 2, depending on the flow case and on the discretization schemes used. The near wall boundary is modeled with a standard wall function and the wall boundary is treated as smooth and adiabatic. For simplicity the flow study has not concerned heat transfer issues Bent pipe geometries The study on gas flow through bent pipes comprised 5 geometries, all 10 mm in diameter with circular cross sectional area. Case 1 was a straight pipe; Cases 2, 3, and 4 consisted of a 15 diameter long straight part followed by a single bend of 30, 60, or 90 degree and finally another 10 diameter long straight section. Case 5 was a double bent pipe having a straight inlet of 12 diameters followed by two 90 degree bends separated by a 2 diameter straight section and then ending up with a 6 diameter long straight part. The five geometries are described in more detail in Table 1. 51

56 Table 1 Description of bent pipe geometries modeled in 1D and CFD Case/ Geometry Length of first Angle of first Radius of curvature Length of second Angle of Radius of curvature for Length of third Number of cells straight part (mm) bend ( ) for first bend (mm) straight part (mm) second bend ( ) second bend (mm) straight part (mm) Geometries 4 and 5 are shown in Figure 11 below. Figure 11 Case 4 with a single 90 degree bend and Case 5 with two 90 degree bends having different radius of curvature. The case 5 geometry was the same as that one used in the work by Hellström [28]. He performed numerical computations on steady and pulsatile flow in both a single and a double bent pipe. STAR-CD was used for this purpose and both the RANS technique with the κ ε RNG turbulence model and the LES approach was tested and the results compared to measured data. A numerical accuracy study was performed and Hellström concluded that using RANS and for the finest grid of the double bent pipe ( cells), the mean numerical uncertainty was 0.02%, 9.6%, and 5.3% at three different evaluation stations. The evaluated parameter was the phase averaged streamwise velocity component. 52

57 Steady flow For the steady flow conditions a symmetric fully developed turbulent velocity profile, from using a power law relation, is imposed as shown in Figure 12. Figure 12 Velocity profile imposed on the inlet to the computational domains. The normal component of the inlet velocity is adjusted to maintain the mass flow rate at a constant value. The mass flow rate corresponded to a mean flow velocity at the inlet of about 240 m/s and a Re number of The outlet to the domain was defined by a pressure boundary at atmospheric pressure and a zero gradient assumption for the temperature and turbulence parameters. The secondary flow structure developed over the bends is a pair of counter rotating vortices, the so called Dean vortices. As the flow enters the bend it is accelerated near the inner wall and decelerated close to the outer wall due to the adverse pressure gradient (which is when the static pressure increases in the direction of the flow). In areas where the fluid is decelerated and its velocity pressure is converted to static pressure a lot of turbulence is produced and significant energy is dissipated. The pressure difference across the pipe induces a fluid motion from the outer wall towards the inner. Further into the bend centrifugal forces comes into play, acting on the fluid in the direction from the centre of the pipe and outward, inducing a fluid motion in the same direction. A secondary flow structure in the form of a single pair of counter rotating vortices is formed, in a plane normal to the primary flow direction. The effect of the secondary flow is to 53

58 transport energy to the inner wall region where low energy fluid is accumulated. Strong secondary flows thereby prevent flow separation which can occur because of the adverse pressure gradient on the inner wall at the bend outlet. Secondary flow causes losses due to mixing in the turning section and in the outlet pipe downstream of a bend. Although the strength of the secondary flow weakens further downstream, a significant part of the losses connected to turning flows occur in the redevelopment region of the flow downstream of the bend outlet. The results show that the secondary flow structure is still present at 10 diameters downstream. Figure 13 shows the mean axial flow velocity and the secondary flow structure for the 60 degree bent pipe at bend inlet, bend outlet, and at two sections downstream of the bend (located at one and three diameters downstream of the bend outlet). Figure 13: Mean flow axial velocity (contoured area) and secondary flow structure (arrows) at bend inlet (upper left), bend outlet (upper right) and at one and three diameters downstream of the bend outlet (lower left and lower right respectively). In addition to the formation of the two vortices, the mean axial velocity profile has changed as compared to that upstream of the bend. The axial velocity profile is distorted and non axis- 54

59 symmetric. It has a higher velocity closer to the outer wall, more or less c-shaped. As the strength of the vortices weakens, so does also the velocity profile even out further downstream. The radial pressure distribution at cross sections upstream and downstream of the bend is affected by the presence of the bend and is non-uniform. The pressure distribution across planes from the 60 degree bend outlet and downstream is shown in Figure 14. Figure 14: Absolute static pressure at the 60 degree bend outlet and 0.5, 1, 1.5, and 2 diameters downstream of the bend (minimum and maximum value for the local static absolute pressure is 0.97 bar and 1.07 bar respectively). The pressure difference across the pipe is nearly 0.1 bar at the bend outlet, one pipe diameter downstream it has decreased to one tenth of that. Performing on-engine pressure measurements it is very important not to place the transducers in or near a bend, especially when investigating low speed and load conditions as the radial distribution might be of importance. Due to the narrow space on an engine this may still not be possible but nevertheless it must be considered. Figure 15 shows the maximum pressure difference over sections, normalized with the mean pressure across the main flow direction, from 3 diameters upstream of the bend to 3 diameters downstream of it for the 60 and 90 degree bent geometries. 55

60 Figure 15 The difference between maximum and minimum pressure is normalized with the average pressure across the main flow direction at sections located from upstream to downstream of the 60 and 90 degree bends of Case 3 and 4. The pressure distribution at sections located at the same distance upstream and downstream of the bend is quite different. The pressure distribution is quite uniform a half to one diameter upstream of the bend, the pressure at corresponding sections downstream of the bend is still quite unevenly distributed. Figure 16 shows how the pressure distribution differs for planes located at 0.5 and 1 diameter upstream and downstream of the 90 degree bend respectively. Figure 16 Absolute static pressure at sections 0.5 and 1 diameter upstream (left figure) and downstream (right figure) of the 90 degree bend. 56

61 To study how the pressure changes along the flow direction the pressure gradient is considered. The gradient of the mass averaged static pressure for sections along the straight inlet part to Cases 3, 4, and 5 are shown in Figure 17. Figure 17 The gradient of the mass averaged (MAV) static pressure along the straight part upstream of the single 60 and 90 degree bend (left figure), and upstream of the first bend and between the two bends of the double bent pipe (right figure). The value for the straight pipe is included in both figures and the bend inlet is positioned at 0 mm. The gradient along the straight pipe, Case 1, is constant and has a value of near (minus) 20 Pa/mm. This figure can be considered a reference value. The corresponding gradient for the single bent pipe geometries is more or less constant and equal to the reference value up to pipe diameters upstream of the bend. This also applies to the first of the bends for the double bent pipe (right figure). Closer to the bend the gradient for the average pressure increases. For the single bent pipes the results show that the sharper the bend the greater the gradient and also the further upstream it has an affect. For the straight part between the two 90 degree bends the pressure gradient is very high close to the first bend outlet, about 10 times that for the straight pipe, and it reduces to the reference level at approximately one pipe diameter downstream. The pressure gradient is not that 57

62 affected by the second bend until very close to the inlet. The gradient along the straight part downstream of the different bends are shown in Figure 18. Figure 18 The gradient of the MAV pressure along the straight part downstream of the single 60 and 90 degree bend and the two 90 degree bends of the double bent pipe. The bend outlet is positioned at 0 mm. It can be seen that the gradient of the mass averaged cross sectional pressure is large in the vicinity of each bend outlet and that the effect of the bend remains almost one pipe diameter downstream of it. The two bends of Case 5 is just about 2 diameters apart and they will most certainly interact with each other and thereby affecting the losses compared to two isolated bends. The pressure gradient after the second 90 degree bend is almost 50% higher compared to the straight pipe still at several pipe diameters downstream, 30 Pa/mm compared to 20 Pa/mm. The velocity and pressure distribution at 1 diameter downstream of the two bends in Case 5 is shown in Figure

63 Figure 19 The pressure and velocity distribution at cross-sectional planes one diameter downstream of the first 90 degree bend (leftmost figures) and the second bend (rightmost figures) of Case 5. The pressure distribution is much more uniform downstream of the second bend compared to the outlet of the first. The secondary flow structure shows a swirling motion compared to the counter rotating vortices downstream of the first bend. This has to do with the skewed velocity profile of the flow entering the second bend. Nearly all the low energy fluid follows the same path, the shortest path between the inside of the first bend to the inside of the other, creating the swirling inplane flow structure Three-dimensional CFD results compared to 1D The geometries according to Table 1 have been modeled in 1D with the same boundary conditions as for the CFD case. The mass flow rate was kept constant at the inlet, the walls were treated as smooth and adiabatic and the outlet pressure was set to atmospheric pressure. The mass flow rate for the double bent pipe was somewhat lower than for the single bent pipes, but equal for the 1D 59

64 and CFD case. The modeled gas properties as molecular weight, specific heat capacity, and dynamic viscosity were set to constant and equal values in both codes. In the CFD code a turbulent velocity profile was imposed at the inlet and in the 1D code a turbulent profile is assumed for values of Re corresponding to turbulent flow. The code accounts for the fact that a turbulent profile has a larger velocity gradient close to the wall, creating additional friction. The absolute pressure at locations along the different geometries is compared for the 1D and 3D CFD calculations, Figure 20. Figure 20 The absolute static pressure at pipe inlet, bend inlet, bend outlet and pipe outlet for the single bent geometries (left figure, 30, 60, and 90 degree bend) and the double bent geometry (right figure, to 90 degree bends). The outlet pressure is set to 1 bar and the upstream pressure for the different pipe geometries is seen to differ for the 1D and CFD calculations. It is quite obvious that the biggest discrepancies are introduced over the bends where the pressure drop is for all cases higher for the 1D code. To make an estimation of the discrepancies introduced on the upstream inlet pressure for the same outlet pressure using the 1D flow assumption together with the use of correction factors and CFD calculations, a non-dimensional pressure parameter is defined according to: p ND p p i out = (48) p out 60

65 This parameter is calculated at the inlet to the geometries using the results from the 1D and CFD calculations and is plotted in Figure 21: Figure 21 Calculated dimensionless pressure parameter from 1D and CFD results at pipe inlet for the different Cases. The relative difference increases with increasing angle of the bend. The discrepancy between the 1D and CFD computational results is highest for the second bend of Case 5. The difference for the calculated non-dimensional pressure coefficients using 1D or 3D computational results is not zero even for the straight pipe. To understand the different upstream results for the pressure using 1D and CFD calculations of flow through these geometries we consider the differences in the pressure gradients along the pipes. The calculated pressure gradient in the 1D code for the simple case of the straight pipe is plotted in Figure 22: 61

66 Figure 22 Pressure gradient along straight pipe modeled with the 1D code. The results show that the code actually has a problem with the number of significant digits. It is not possible as a user to set that parameter and with a small discretization length of 1 mm as used, pressure jumps appears over the pipe length. The value for the pressure gradient is just about the same as the value for the gradient of the averaged cross sectional pressure in the CFD calculations, about 20 Pa/mm. The 1D flow approximation for a straight pipe is shown to be very good and more or less as expected. The calculated pressure gradient for all straight parts of the geometries in Table 1 is exactly the same as for the straight pipe modeled alone. This means that modeling a straight part next to a bend in 1D, a distance of diameter upstream or downstream of that bend will have a calculated pressure gradient that is lower compared to 3D computations. The 1D code does not account for the presence of a neighboring bend. It is seen in Figure 20 that the largest differences between the calculated upstream pressure for Cases 1 to 5 is the pressure drop over the bends. The results for the pressure drop over the various bends from 1D and CFD calculations are shown in Figure

67 Figure 23 The absolute pressure drop (left figure) and the average pressure gradient (right figure) over the bends of Cases 2, 3, 4, and 5. The pressure drop is displayed as an absolute value in kpa over the entire length of the bend. Cases 1 to 5 correspond to the 30, 60, and 90 degree single bends and the two 90 degree bends of the double bent pipe. The discrepancy between the two codes is quite big. A global mean value for the pressure gradient from dividing the pressure drop over the bend by the length of the bend is plotted in the right figure and displayed in Pa/mm (compare with the results shown for the resolved pressure gradient of the straight parts connected to the bends, Figure 17-Figure 18). The pressure gradient over the bent pipes is in all cases much higher in the 1D code compared to the 3D code. As secondary flow structures develop through these pipes the 1D code relies on correction of the pressure loss in the momentum equation by adding a semi-empirical pressure loss coefficient C p. The coefficient is interpolated in a look-up table from the radius of curvature and the length of the bend. According to support it is based on an average of a few published sources, as they were not in complete agreement. The SW vendor is working on improving the model and is adding a missing Re dependence. The pressure loss coefficients for the single bent geometries are calculated according to equation (33) using 1D and 3D data and the result is plotted in Figure 24 together with the tabulated values used by the 1D simulation. Included in the diagram are also 63

68 estimated values for the loss coefficients using bend performance charts from experiments by Miller [43]. 0.4 Loss coefficient [-] D calc from data 1D tabulated 3D bend inlet to bend outlet 3D bend inlet to 1d down stream Bend performance chart Bend angle [degree] Figure 24 Calculated loss coefficients for the single bent geometries using 1D and 3D data, the 3D case even for including the losses up to 1 diameter of the downstream connected pipe. Tabulated loss coefficients used in the 1D simulation are also displayed together with estimated values of the loss coefficients from using bend performance charts based on experiments by [43]. Measurements are made on steady incompressible flow of a nearly Newtonian fluid flow through various bends connected to long inlet and outlet pipes (more than 50 diameter long), the Re number is in all cases For a Newtonian fluid the relation between the shear stress and the strain rate is linear, the viscosity being the proportionality constant. Basic loss coefficients for bends based on these measurements are tabulated in a chart. The basic loss coefficients can then be corrected to account for other values of the Reynolds number, the length of the inlet and outlet pipe connected to the bend, surface roughness, bend-to-bend interactions, and even to compressibility effects for Mach numbers above 0.2. The corrections that can be made are further described in the Appendix. Before commenting on the results it must be pointed out that, still writing this thesis, it is not known exactly how the different variables were measured (how the velocity was measured / if the 64

69 velocity profile was measured) or any detailed description of the measurement installation system that was used producing the tabulated values for the loss coefficient by [43]. The 1D tabulated loss coefficients are expected to be close to the values of the performance charts as that kind of data is described as being used by the 1D software support. Why the performance chart data estimates even higher losses over the bends is probably due to the correction factors that have been used from the basic chart data. The tabulated values used in the 1D code are very close the measured uncorrected loss coefficients. Compensating for the lower Re number has the affect of increasing the basic loss coefficient (a factor of about 1.6 for these cases) and the correction for the only 10 diameter long outlet pipe has the affect of decreasing the basic loss coefficient (a factor between for the different cases). Finally, compensating for compressibility effects has the affect of decreasing the losses with a factor close to The 1D tabulated values and the calculated pressure loss coefficient using 1D result differ and the latter is more close to the chart data. There are large discrepancies found comparing the 1D tabulated coefficients and calculated values using 3D data. To see if the 1D code perhaps overestimates the loss coefficient of a bend to include the losses connected to the downstream pipe, the total loss coefficient of the bend plus 1 diameter of the pipe downstream of it, is calculated in 3D and displayed in the diagram, Figure 24. Not even by including the losses one diameter downstream of the bend gives good agreement between 1D and 3D results. Experimental observations by [43] on circular cross sectional 90 bends show that the distribution of losses in the bend and its outlet pipe, for a radius of curvature between 0.8 and 1.5, about 80% of all the losses occur in the bend and the first 2 pipe diameters downstream of the bend outlet. As the bend angle is reduced below 90 the percentage of the total loss occurs in the downstream pipe. For a 45 bend with a radius of curvature below 3, as much as 50% of the loss is connected to the downstream pipe. It is not understood why the loss coefficients from performance chart data and 3D calculated result differ that much. As mentioned it is not known how the measurements on the pipe bends were performed and measurements on the same geometries as those being modeled in 1D and 3D is needed to validate the simulation results for a deeper analysis (hopefully to be included in the continuing work). Perhaps the loss coefficient calculations are not appropriate to use directly on 65

70 3D data because of the averaging process of the flow variables that must be carried out at the cross-sectional planes at the bend inlet and outlet where the flow has a skewed velocity profile and strong secondary flow. The results for the loss coefficients for the two bends of Case 5, bend 1 and 2, is shown in Figure 25. Loss coefficient [-] Bend nr [-] 1D calc from data 1D tabulated 3D bend inlet to bend outlet 3D bend inlet to 1d ds bend outlet Bend performance chart Figure 25 Calculated loss coefficients for the 2 bends of geometry 5 using 1D and 3D data, the 3D case even for including the losses up to 1 diameter of the downstream connected pipe. Tabulated loss coefficients used in the 1D simulation are also displayed together with estimated values of the loss coefficients from using bend performance charts based on experiments by [43]. The 1D code s tabulated value for the loss coefficient of the second bend is lower compared to that of the first bend, whereas the 3D results shows a small increase of the loss coefficient of the second bend compared to the first. In the 1D simulation the velocity profile into the second bend is identical to the one entering the first bend, no bend interactions are considered. This explains the lower pressure drop for the second bend due to the larger radius of curvature compared to the first bend. In the CFD simulation it is shown that the flow into to the second bend is not identical to the inlet of the first bend and the velocity profile is asymmetric, Figure 19. The performance charts result shows the same effect, that the loss over the second bend is higher than the first. This is without using available correction factors on the loss coefficient for bend-bend interactions, only 66

71 for inlet and outlet pipe length which is different in this case. Interactions between two bends occur if a second bend is located in the flow redevelopment region downstream of the first bend and then the loss connected to that region is decreased. Also the velocity profile in the redevelopment region is different to that of an isolated bend which will affect the second bend. Direct interaction between two bends can both have the effect of decreasing and increasing the pressure loss compared to isolated pipes [43]. Investigating the different terms in the expression for the pressure loss coefficient the same trends are shown for the 1D and 3D computations except for the total pressure at the outlet of the second bend. It is the dynamic pressure contribution to the total pressure at the outlet of the second bend that gives the different results for the second bend of Case 5: Figure 26 The dynamic pressure (multiplied by a factor 2) at the first and second bend outlet of Case 5. The dynamic pressure in STAR-CD is calculated using the three components of the velocity vector and it as the area averaged value over the section upstream/downstream of the bend. Mass averaged values are used in the calculations displayed in Figure 24 and Figure 25 and they had a little affect on the calculated loss coefficient. Even though the exact levels are not the same for the 1D and CFD, Figure 26 shows that the dynamic pressure shows the same trend at the bend inlet and also at the outlet for the single bent geometries. The CFD results for the double bent pipe 67

72 show that the dynamic pressure at the outlet of the second bend is higher compared to the first bend, a result that is contradictory to what the 1D results show. One of the causes to the discrepancies between the calculated pressure gradient using 1D or 3D CFD calculations is assumed to be secondary flow effects as they are not accounted for in the 1D code, yet corrected for. The strength of the secondary flow close to the inlet and the outlet of the bends to Cases 2, 3, 4, and 5 are calculated according to 27. u 2 u 2 + v + v w 2 and are plotted in Figure Figure 27 Strength of secondary flow upstream and downstream of bends to Cases 2-5. The strength of the secondary flow along the inlet to the various bends (left figure) is more or less equal for all the cases except for the inlet to the second bend of Case 5 which is much higher. A slight increase for a larger degree of bend is seen. The results are more spread along the outlet to the bends (right figure) but still the strength of the secondary flow is higher for larger degree bends. The secondary flow at the outlet to the second bend is shown to be much lower compared to the outlet of the first 90 degree bend which in turn is more or less identical to the outlet of the single 90 degree bend. The level of the secondary flow at the outlet to the second bend is even lower than for the 60 bend case. 68

73 Pulsating flow Case 5 in Table 1 is simulated with pulsating flow in both 1D and 3D. The mass flow rate at the inlet boundary for the five computed engine cycles are shown below, the individual cycles are displayed on top of each other: Figure 28 Inlet boundary mass flow rate for each of the five engine cycles run, the individual cycles are laid on top of each other. The mass flow rate is imposed by providing boundary values for the inlet density and the inlet velocity. The imposed velocity profile is fully turbulent and is a function of radius and time according to Figure 29. Figure 29 The inlet boundary normal velocity component as a function of radius and time given at the inlet boundary to Case 5 for the pulsating flow case. 69

74 The Reynolds values are up to during the pulse. The results for the pulsating flow case is presented in Figure 30 and Figure 31 where the secondary flow at sections immediately downstream of the first and second bend is plotted at 4 different times during the pulse. To get a better picture of the magnitude of the axial velocity the secondary flow is here defined as 2 2 u + v w 2. Figure 30 The strength of the secondary flow at the first bend s outlet at 4 different times during the pulse. These time steps correspond to low (upper left), medium (upper right), high (lower left) and again low (lower right) mean axial velocity. 70

75 The upper part of the planes depicted in the figure correspond the outer curvature of the bend and the lower part the inner curvature. The secondary flow is less pronounced in regions where the axial velocity is higher (having the C-shaped velocity profile out of the first bend in mind). At the outlet to the second bend the results look somewhat different, Figure 31. Figure 31 The relative strength of the secondary flow at second bend outlet at 4 different times during the pulse. As was noted for the steady-state flow of Case 5 (Figure 27), the strength of the secondary flow both upstream and downstream of the two bends is different from each other. With pulsating flow the strength of the secondary flow is weaker downstream of the second bend compared to downstream of the first bend. The upper part of the cross-section is the outer curvature and the high velocity region is rotated to the right as compared to the first bend, Figure

76 Full CFD results compared to 1D To compare the results of the pulsating flow using 1D and CFD computations, the instantaneous values of the calculated pressure drop over the two bends of Case 5 is plotted in Figure 32. The mean axial velocity at the respective bend inlet is also displayed. Figure 32 A comparison between the simulated instantaneous pressure drop over the first bend (left) and the second bend (right) of Case 5 using 1D and CFD calculations. The axial velocity at the two bend inlets is shown as well (right y-axis in the two plots). As for the steady-state flow case, the 1D code estimates a higher pressure drop over each of the two bends compared to the CFD code. The discrepancies between the 1D and CFD results are a somewhat larger for the first bend Exhaust manifold Steady flow The exhaust manifold of the engine that has been analyzed both by on-engine measurements in test cell and by 1D engine simulations will be studied with the aid of CFD computations. The exhaust manifold geometry that we consider is shown in Figure 33: 72

77 Figure 33 The exhaust manifold geometry. The exhaust manifold consists of two separate parts. They do not join before the turbine inlet. For simplicity a first study was made only considering the two outer runners, the primary exhaust pipes of cylinders 1 and 4. The mass flow rate was imposed at the two inlets and a constant pressure was set at the outlet. The mass flow rate was kg/s at one inlet and almost zero at the other, by imposing the velocities and densities given at the boundaries. The corresponding Reynolds number is about The outlet pressure was set to atmospheric pressure and the walls were considered to be smooth and adiabatic. A plug-flow profile was set at the inlet boundaries to the extension volumes added to the original geometry. The computational domain was extended with the aim of allowing the flow to develop naturally from the inlet; however, the extended inlets were not long enough to produce a fully developed turbulent velocity profile at the original geometry s inlet. Similar extension of the outlet section was aimed at avoiding the formation of a separation bubble that extends up to the outlet boundary. It has to be noted that such a separation bubble is formed due to the strong bend of the exhaust manifold ahead of the inlet to the turbine. Separation of the flow gives flow losses due to large scale mixing spreading through the main flow and results in a drop in total pressure. The static pressure at a section across the computational domain is shown in Figure

78 Figure 34 The absolute static pressure distribution (Pa) at a section across the outer exhaust runners. There are large pressure variations across the right bend which is connected to cylinder 1. The bend is about 75 and counter rotating vortices are seen downstream of the bend. At the outlet, downstream of the junction joining the two pipes, the secondary flow structure is a swirling motion. The axial velocity component is also very asymmetric, Figure 35. Figure 35 Flow structure at the original outlet of the junction joining the outer runners to cylinders 1 and 4 (the CFD domain outlet is extended 120 mm downstream of the original geometry). The axial velocity is shown as a contour plot and the secondary flow components as vectors. 74

79 The strength of the secondary flow is locally as or even larger than the axial velocity component, which is seen in, Figure 36, showing the secondary flow at the junction of the exhaust pipes of cylinders 1 and 4. Figure 36 The strength of the secondary flow at the junction outlet of cylinders 1 and CFD results compared with 1D results The outer runners of the exhaust manifold are modeled in 1D with the same constant inlet mass flow rate and outlet pressure as for the CFD model. The walls are assumed to be smooth and adiabatic. The calculated pressure drop, from the inlet of the runner blowing with high velocity to the junction outlet, is 20% lower in the 1D calculations compared to the CFD calculations. From previous investigation of the pressure losses over the various bent geometries under steady-state flow conditions it was expected that the pressure loss calculated by the 1D code would be larger as compared to the CFD results. The fact that the opposite is true for this particular geometry may depend on differences in the problem set-up. For example GT-Power assumes a fully turbulent velocity profile which do account for additional frictional losses to the wall, but since a plug flow is 75

80 used in the CFD calculations, there are large initial pressure gradients as the turbulent flow develops. In addition, the flow itself is poorly modeled in 1D. The CFD geometry has not circular cross sectional shape which is assumed by the 1D code and correction factors have not been used in this case to account for other shapes. Also the bend angle is not easy to account for (as shown in this thesis above). Handling the junction in the 1D model is very intricate and it is done by ad-hoc fixes. The pressure drop over the runner from cylinder 4 with almost zero mass flow rate is again larger in the 1D calculations as compared to the CFD calculations. Running the CFD model with a turbulent velocity profile at the two inlets would answer the question if the profile has that significant effect on the pressure losses or if it is the conversion of a complex geometry with bent pipes, irregular cross sectional area and junctions that is the main problem Pulsating flow For the simulation of pulsating flow through the outer runners of the exhaust manifold, inlet boundary condition is extracted from 1D engine simulations at pipe components located upstream of the manifold, Figure

81 Figure 37 Inlet boundary conditions at the two outer primary pipes of the exhaust manifold, velocity, density, and temperature profiles. They are extracted from 1D engine simulations at 1300 rpm and wide open throttle. The imposed pressure at the outlet is also extracted from 1D simulation and is time-dependent. The shape of the inlet velocity profile contains only a constant axial component (i.e. plug flow) and the Reynolds number varies between 0 and during the pulse. The figure below (Figure 37) shows a plot of the axial velocity together with secondary flow vectors for low, medium and high mass flow rates at the junction outlet. 77

82 Figure 38 Velocity field at the junction outlet. Axial velocity is shown as a contour plot and secondary flow components as vectors. At very low mass flow rates the flow detaches from the wall and reverses during the cycle. Thus, the outlet boundary becomes an inlet boundary and that the temperature and velocity must be given in addition to the pressure at the outlet boundary (from the 1D simulation). This may give rise to sudden temperature changes on the boundary as the temperature drop is not identical in the two codes. This is since the temperature on the outlet boundary is calculated by STAR-CD for positive outflow and it is imposed, using temperatures from GT-Power simulations, for reverse flow situations. An improved method for imposing the outlet temperature is desirable. For very low mass flow rates the flow is dominated by the in plane velocities and for medium and high mass flow rates the main flow normal to the boundary has a secondary flow structure of swirling motion. 78

83 The strength of the secondary flow varies and is shown for medium and high mass flow rates in Figure 39. Figure 39 Strength of the secondary flow velocity for medium and high axial velocity Flow in manifold versus 1D The results from comparing the 1D and CFD overall pressure drop, from the inlet of the primary exhaust pipe of cylinder 1 to the outlet of the junction, during one engine cycle is plotted in Figure 40. Figure 40 Comparison between 1D and CFD calculated time resolved pressure difference across the manifold (primary pipe connected to cylinder one and outlet to junction of cylinder 1 and cylinder 4) over one engine cycle. 79