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A sectoral approach to modelling wall heat transfer in exhaust ports and manifolds for turbocharged gasoline engines.

ABSTRACT

A new approach is presented to modelling wall heat transfer in the exhaust port and manifold within 1D gas exchange simulation to ensure a precise calculation of thermal exhaust enthalpy. One of the principal characteristics of this approach is the partition of the exhaust process in a blow-down and a push-out phase. In addition to the split in two phases, the exhaust system is divided into several sections to consider changes in heat transfer characteristics downstream the exhaust valves. Principally, the convective heat transfer is described by the characteristic numbers of Nusselt, Reynolds and Prandtl. However, the phase individual correlation coefficients are derived from 3D CFD investigations of the flow in the exhaust system combined with Low-Re turbulence modelling. Furthermore, heat losses on the valve and the seat ring surfaces are considered by an empirical model approach.

Since the comparison between measured and simulated exhaust temperature at turbine inlet serves as an evaluation criterion, a detailed 1D thermocouple model is implemented. Exothermic exhaust after-reactions are represented by a reduced reaction kinetics mechanism. The investigations were carried out for four TC-DI gasoline engines. The low scattering of the correlation coefficients as well as the high agreement between simulated and measured exhaust temperature verify the model quality. Overall, the new sectoral approach shows a significant improvement of wall heat flux calculation in comparison to conventional single-phase approaches from literature.

CITATION: Franzke, B., Pischinger, S., Adomeit, P., Schernus, C. et al., "A Sectoral Approach to Modelling Wall Heat Transfer in Exhaust Ports and Manifolds for Turbocharged Gasoline Engines," SAE Int. J. Mater. Manf. 9(2):2016.

INTRODUCTION

The 1D gas exchange simulation is an established CAE tool in the design process of turbocharged gasoline engines. Thereby, the precise calculation of the thermal exhaust enthalpy plays an important part to optimize engines with focus on future challenges like C[O.sub.2] - emission limits and real drive emissions combined with the WLTP driving cycle. On the one hand the available level of thermal exhaust enthalpy affects the TC matching process to ensure performance targets; on the other hand the required fuel enrichment for TC protection is typically determined by means of turbine inlet temperature. Against this background a new sectoral 2-phase wall heat transfer model was developed for the exhaust port and manifold to improve result quality of 1D gas exchange simulation.

FUNDAMENTALS

In 3D CFD simulation with Low-Re turbulence modelling, the conservation equations are solved in the boundary layer up to the viscous sublayer. The abstinence of wall function enables a very accurate calculation of heat transfer. Using near-wall cell data the local heat flux is determined by the following equations:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

In 1D simulation there is no detailed information about the boundary layer available. Therefore, a simplified approach is required. The convective wall heat flux is calculated using gas temperature TG and wall temperature T :

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The determination of the heat transfer coefficient [alpha] (HTC) is based on the similitude theory via the Nusselt number which is estimated from approaches like the Colburn analogy [1]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

or empirical correlations in terms of:

N[u.sub.L] = C [Re.sub.La] [Pr.sup.b](6)

Conventional Nusselt correlations for turbulent pipe flows like the one from Gnielinski [2]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

are not sufficient for describing the heat transfer in exhaust ports and manifolds of combustion engines. The reason for this is the flow profiling which is caused by the high velocity flow around the exhaust valves in combination with the curved port shape. Additionally, a high level of turbulence intensity is generated by the flow around the valves. Both effects lead to a significant enhancement of the heat flux in comparison to conventional turbulent pipe flows.

This correlation was already detected by Zapf in the 60s of the last century and he derived his famous correlation for the HTC in the exhaust port as a function of valve lift and mass flow rate [3].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

Further correlations for heat transfer in the exhaust system were developed by Shayler et al. [4]

N[u.sub.D] = 0.18 R[e.sub.D](9)

as well as Depcik and Assanis [5]: N[u.sub.D] = 0.07 [Re.sub.D][degrees]0.75 (10)

Besides, Heller has derived an extended correlation from heat flux measurements which considers the curvature of the exhaust manifold pipes. The approach includes an effective Reynolds number which is calculated from a specially defined effective velocity in order to incorporate the pulsating character of the exhaust flow [6]. In this context, index "n" represents the current time step and "n-1" the previous one.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

INVESTIGATED ENGINES AND CORRESPONDING MODELS

The investigations were carried out at four turbocharged gasoline engine with direct injection. The test carriers consist in pairs of engines with conventional and with integrated cooled exhaust manifolds. The technical specifications are summarized in table 1.

The analysis of heat transfer is based on six different operating points; four full load and two part load points, see table 2.

To measure exhaust temperatures at turbine inlet, the engines are equipped with a thermocouple (type K) with a diameter of 3 mm and a penetration depth of 15 mm. In addition, several surface thermocouples are mounted on the exhaust manifold outer walls to obtain information about the wall temperatures.

3D CFD Model

In addition to the flow guiding surfaces, the CFD exhaust manifold models include the thermocouples at the identical location as the hardware on test bench. The simulations are run with the RANS k-[omega]-SST turbulence model by Menter [7] in combination with Low-Re wall treatment. Detailed mesh refinement near the walls as well as in the surroundings of the thermocouples ensures that the condition [y.sup.+] < 1 is fulfilled for any wall cells. An exemplary section of the polyhedral mesh is represented in figure 1.

A new approach to set realistic inlet boundary conditions was applied by extracting data from in-cylinder flow simulations. For that purpose a section plane was defined downstream the exhaust valves, see figure 2. Profiles of mass flux, total temperature and the turbulent quantities k and [omega] were written out for a complete cycle as a function of a local coordinate system. This section plane is likewise the inlet of the CFD exhaust manifold model. Due to the identical coordinate system, the profiles can be mapped directly on the cell faces.

1D Gas Exchange Model

The gas exchange models were calibrated by test bench data with the use of measured quantities like air mass flow rate, injected fuel mass, valve timings, TC speed and several pressure and temperature values. The in-cylinder heat release rates of the six investigated operating points are determined by cylinder pressure analysis from measured indication data.

1D Thermocouple Model

The accordance between measured and calculated exhaust temperature at turbine inlet is used as a criterion to evaluate the quality of the heat transfer model. Therefore, the measurement characteristics of a thermocouple have to be considered in the gas exchange model. The measured temperature of a thermocouple is influenced by thermal inertia, radiation with surrounding walls, heat conduction into the wall and the convective heat transfer from the fluid. The thermocouple temperature [T.sub.T] can be determined by solving the following differential equation with the variable z for the thermocouple penetration length:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

The convective term of the equation is extended by the factor [B.sub.F]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

The factor is defined as the relation between the local and the average heat transfer coefficient at a specific position z along the penetration length. In this manner the 3D flow characteristic at sensor position can be also considered in 1D simulation. The average HTC [bar.[alpha]] is typically calculated by a Nusselt number correlation for a circular cylinder in cross flow For this the authors propose the following correlation, which was derived from previous CFD LES investigations of wall mounted cylinders with low height/diameter ratio in steady-state flow:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14) Further details regarding the LES investigations as well as the derivation of equation 14 will be published by the authors in future.

The partition of the thermocouple in sections with a length of 1 mm leads to a [B.sub.F] map for an entire engine cycle as it is shown exemplary in figure 3:

Previous investigations in steady-state flow on a hot gas test bench have proved that the presented 1D thermocouple model achieves a very high accordance between measured and calculated temperature values ([DELTA]T < 4 K).

Exhaust After-Reactions

The existence of species like unburnt hydrocarbon (HC), CO and [H.sub.2] ]in the exhaust gas enables exothermic after-reactions which increase the thermal exhaust enthalpy. Especially the combination of scavenging due to positive valve overlap and a rich in-cylinder mixture leads to a significant rise of thermocouple temperature at turbine inlet of up to 80 K. The complex reaction kinetics can be modelled precisely by detailed reaction mechanism. However, this results in an unacceptable large simulation duration for 1D gas exchange calculation. Therefore, a reduced iso-octane mechanism by Heufer [8] was implemented in the gas exchange model. In figure 4 there is a comparison between a detailed mechanism by Andrae [9] and the reduced one by Heufer by means of 3D CRFD simulations for two exemplary operating points of engine B.

Despite the slight differences in the traces, there is a good agreement in the integrated released amount of energy. Hence, the reduced mechanism represents a reasonable trade-off between simulation duration and accuracy.

CORRELATIONS OF WALL HEAT TRANSFER

Methodology

The flow around the exhaust valves generates a profiling as well as high level of turbulent kinetic energy (TKE). Downstream the valves the flow becomes more and more homogeneous and TKE is dissipating partially. Therefore, the heat transfer cannot be described precisely by a unique correlation. As a part of the CFD analysis, in figure 5 the TKE level of different section planes downstream the exhaust valves is presented. It can be seen that the TKE level is dropping with increasing distance to the exhaust valves. Only a slight renewed increase is caused by the junction at position 6.

Therefore, the exhaust system is divided into characteristic sections which are shown in figure 6:

The exhaust port consists of "Section 1" and "Section 2"; the exhaust manifold is separated in straight and curved sections of the runner. Furthermore, the section downstream the junction of the runners is designated "Turbine Inlet".

In addition to the spatial partitioning of the exhaust system, the exhaust process can be subdivided temporally in two flow phases:

* The blow-down phase with Mach = 1 in valve gap

* The push-out phase with Mach << 1 in valve gap

The two phases are explained in figure 7 by means of data of the exhaust valve object in 1D gas exchange simulation of engine A:

In blown-down phase the flow rate through the valve gap is restricted by the speed of sound (Mach = 1) since there is a supercritical pressure ratio. In push-out phase the pressure ratio is subcritical; hence the flow velocity is significantly lower (Mach <<1).

The different levels of flow velocity in the two phases generated different intensities of TKE and flow profiling. For this reason it makes sense to correlate the heat transfer also individually for each phase.

The general approach of the Nusselt number correlations has always the following form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

The mathematical determination of the parameters C and a is achieved by the least squares method in combination with a square weighting of the heat flux:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

The analysis of the wall heat transfer in the CFD models occurs in a small sub volume which is equal to the typical discretization length in 1D simulation. A surface averaging of the heat flux and a mass flow averaging of Reynolds and Prandtl number as well as fluid temperature and heat conductivity provide the required data for the derivation of the correlations. The wall temperatures in the water cooled sections in the cylinder head are estimated basing on data from previous FEM analysis. For the sections outside the cylinder head the measured temperatures from the surface thermocouples are used.

Exhaust Port

Section 1

This section comprises in a 4-valve concept the pipe section starting from the exhaust valve up to the junction of the ports. The figure 8 shows the CFD calculated wall heat flux and the corresponding correlation for a two- and single-phase approach for the six investigated operating points of engine A.

It is apparent that the 2-phase approach enables an excellent agreement with the CFD data over the entire exhaust process. As a consequence of the heat flux weighting, the single-phase approach fits also well in the blow-down phase. However, the discrepancies in the push-out phase are inevitable due to the different flow characteristics in each phase mentioned above. The correlation quality of the low part load operating point 2000 rpm / BMEP = 0.20 MPa is lower than for the remaining points. The weak intensity of the blow-down and the multiple reversals of the flow direction during the long push-out phase result in poorly structured flow characteristics which are unfavorable for correlation between Nusselt and Reynolds number. As a consequence, this part load operating point is neglected regarding averaging.

The correlation results have shown that the prefactor C in the equation (15) can constantly be set to a value of 0.15. Consequently, only the exponent of the Reynolds number a has to be determined for each section and phase. In figure 9 the scattering of the operating point individual correlations is plotted for engine A.

The scattering has a magnitude of [+ or -]7 % for the 2-phase approach. The total scattering between the four engines is evaluated by the coefficient of variation (CV):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

The scattering is plotted in figure 10. The level of CV is very low which can be applied for a universal set of correlation parameters.

Section 2

This section comprises the range downstream the junction of the port. The scattering plot in figure 11 reveals a comparable level of the CV as in the case of "Section1". The exponents of the Reynolds number in the first phase are slightly higher than for the previous section. The enhanced HTC results from an increased surface area in combination with the still very intense turbulence level.

Exhaust Manifold

Runner - Straight

As a consequence of the decrease in flow profiling and turbulence level, the HTC is dropping in the exhaust manifold runners. Hence, the Reynolds number exponents have lower values than in exhaust port sections. The coefficients of variation of the exponents have the same order of magnitude, see figure 12.

Runner - Curved

The investigated runner sections have a radius of curvature in the range of 35 mm < R < 100 mm. Pipes with larger radii are assigned to the section "Runner - straight". For this reason curved runners can only be found in the engines B and C. The corresponding scattering plots are shown in figure 13:

The analysis has revealed that in the first phase the HTC is slightly lower in the curved section than in the straight one. This is not in contradiction to previous findings. In detailed investigations of turbulent flows in coiled pipes, Guo et al. have determined the following correlation [10]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

This correlation is compared with the one for straight pipes by Gnielinski - equation (7) - in figure 14:

It can be seen that the heat transfer in straight pipes becomes larger than for curved pipes for Reynolds numbers > 50.000. During the heat transfer dominating blow-down phase there are Reynolds numbers above this value for full load and upper part load. In contrast, the exponents of the second phase are approx. equal as a consequence of the lower Re level while pushing out.

Turbine Inlet

This section covers the range downstream the junction of the runner up to the volute of the turbocharger. The heat flux can be correlated by a 1-phase approach with a sufficient accuracy. A 2-phase approach is not required in this section, see figure 15:

The scattering plot in figure 16 shows the highest level of CV in comparison to the other sections. Additionally, the exponents are slightly larger than in the runner sections. Both effects are caused by the design of the junction which is individual for every engine. It has been already discussed by means of figure 5 that the design of the junction leads to an increase of turbulence which enhances wall heat transfer. The non-uniform design is responsible for the different intensity of turbulence enhancement which eventually results in the slightly increased scattering.

Universal Correlation Parameters

The following table summarizes the universal parameters of the Nusselt number correlations (mean values in the scattering plots) for each section:

COMPARISON WITH APPROACHES FROM LITERATURE

The sectoral 2-phase heat transfer model is compared with existing single-phase approaches from literature. In figure 17 a profile of the Reynolds number in the exhaust port is used to calculate the HTC:

The approach by Zapf (Eq. 8) overestimates the HTC for the entire exhaust process. In contrast, the correlation for conventional turbulent pipe flow by Gnielinski (Eq. 7) underestimates the heat transfer significantly. The approach by Shayler at al. (Eq. 9) shows a good agreement in the blow-down phase, but less accordance in the push-out phase. A contrary tendency can be found in the correlation by Depcik et al. (Eq. 10) with its excellent agreement in push-out phase.

In addition, the comparison is carried out for the curved runner section in figure 18:

Analogous to the exhaust port, there is also an underprediction of the HTC in blow-down phase for the correlation of the conventional turbulent pipe flow. However, the solution by Gnielinski fits well to the 2-phase model in the push-out phase. The approaches by Depcik et al. and Heller (Eq. 11) differ only marginally, but both are slightly overestimating the HTC consistently.

The conclusion of the comparisons is that the single-phase approaches from literature are not sufficient for achieving a good agreement in the entire exhaust process. The benefit of the 2-phase approach is the higher flexibility which enables a consideration of the different heat transfer characteristics in blow-down and push-out phase.

HEAT LOSSES AT EXHAUST VALVE AND SEAT RING

In addition to the wall heat losses in exhaust port and manifold, there is also heat transfer from the fluid to the surfaces of the valve and the seat ring. Figure 19 shows the total temperatures in the exhaust port 25 mm downstream the valves. Without a consideration of the heat losses ("uncorrected"), there is a significant discrepancy in the temperature between 3D and 1D simulation, especially in the early phase of valve opening. For this reason the heat transfer model is extended by an empirical approach to include the impact of these heat losses:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

The factor y which is calculated by the Nusselt number correlation of "Section1" enhances the HTC. The factor is a function of the exhaust valve lift and its profile can be found in figure 20. The heat transfer enhancement is restricted to the first 25 mm of the exhaust port.

With increasing valve lift, the heat losses at valve and seat ring become very small in relation to the total enthalpy passing the valves. Therefore, the factor has a declining trend for rising lift.

EXHAUST TEMPERATURES

Finally, the sectoral 2-phase heat transfer model is to be evaluated based on a comparison between the measured and calculated thermocouple temperatures at turbine inlet. The difference between both values is plotted in figure 21. Furthermore, there is a differentiation between the individual correlation parameters for each engine and operating point according to the symbols in the scattering plots and the universal correlation parameters according to table 3.

The individual parameters represent the highest feasible accuracy due to the highest level of detail. The mean discrepancies at full load are only 2.6 K and at part load 7.9 K. As expected, the universal correlation parameters show a slight increase in the mean discrepancy (3.1 K at full load; 9.5 K at part load). However, accuracy is still excellent considering the typical range of tolerances in a 1D simulation. Accordingly, the very good agreement in measured and calculated exhaust gas temperatures can be regarded as a verification for the model quality. The sectoral heat transfer model is an important module relating to a precise determination of exhaust enthalpy and temperature in 1D simulation.

SUMMARY

In this paper a new sectoral heat transfer model for 1D simulation is presented. The model subdivides the exhaust system geometry into characteristic sections. In addition, the exhaust process is separated in two flow phases: blow-down and push-out phase. Correlations of the Nusselt number are used for the heat transfer in each section and phase individually. The parameters of the correlations are derived by analysis of the heat flux data of previous 3D CFD exhaust system simulations. The low scattering between the four investigated TCGDI engines enables the determination of a universal set of correlation parameters. Thus, no distinction between integrated and conventional exhaust manifolds is required. The heat transfer model is completed by an empirical heat transfer enhancement factor to consider heat losses at the surfaces of the exhaust valves and seat rings.

A comparison with existing approaches from literature shows that the sectoral model enables a more accurate modelling of wall heat transfer over the entire exhaust process due to its higher level of detail. Generally, single-phase approaches provide only feasible results either in blow-down or push-out phase.

Furthermore, in the 1D gas exchange model there is a detailed 1D thermocouple model as well as a reaction mechanism to consider exhaust after-reaction implemented. Thereby, the agreement between measured and calculated thermocouple temperature is used to evaluate model quality. The low temperature difference (< 10 K at full load) between measurement and simulation verifies the accuracy of the sectoral heat transfer model. Thus, the model is a key part within the 1D gas exchange calculation for a precise determination of thermal exhaust enthalpy.

REFERENCES

[1.] Colburn, A. P., "A method of correlating forced convection heat transfer data and a comparison with fluid friction". Trans. AIChE, 29, 1933.

[2.] Incropera, F. P. and DeWitt, D. P., "Fundamentals of Heat and Mass Transfer",6th ed., 2007

[3.] Zapf, H., "Untersuchung des Warmeuberganges in einem Viertakt-Dieselmotor wahrend der Ansaug- und Ausschubperiode", PhD Thesis, Technical University Munich, 1968

[4.] Shayler, P., Chick, J., and Ma, T., "Correlation of Engine Heat Transfer for Heat Rejection and Warm-Up Modelling," SAE Technical Paper 971851, 1997, doi:10.4271/971851.

[5.] Depcik, C. and Assanis, D., "A Universal Heat Transfer Correlation for Intake and Exhaust Flows in an Spark-Ignition Internal Combustion Engine," SAE Technical Paper 2002-01-0372, 2002, doi:10.4271/2002-01-0372.

[6.] Heller, S., "Analyse und Modellierung des instationaren Warmeubergangs in der ottomotorischen Abgasanlage", PhD Thesis, Technical University Munich, 2009

[7.] Menter, F. R., "Two-equation eddy-viscosity turbulence modeling for engineering applications", AIAA Journal, vol. 32, no. 8, 1994

[8.] Heufer, K. A., "Quasi-Global Kinetic Modeling of Auto-ignition of Fuels", Symposium for Combustion Control, Aachen , 2015

[9.] Andrae, J., Brinck, J. and Kalghatg, G.,"HCCI experiments with toluene reference fuels modeled by a semidetailed chemical kinetic model", Combustion and Flame 155, 2008

[10.] Guo, L. et al., "Transient convective heat transfer in a helical coiled tube with pulsatile fully developed turbulent flow", Int. Journal of Heat and Mass Transfer, Vol. 41, 1998

CONTACT INFORMATION

Bjoern Franzke Institute for Combustion Engines, RWTH Aachen University

franzke@vka.rwth-aachen.de

DEFINITIONS/ABBREVIATIONS

a - Exponent of Reynolds Number

BMEP - Brake Mean Effective Pressure

C - Prefactor

c - Specific Heat Capacity (Solid)

cf - Friction Coefficient

c - Specific Heat Capacity (Fluid)

CA - Crank Angle

CFD - Computational Fluid Dynamics

CRFD - Comp. Reactive Fluid Dynamics

D - Diameter

h - Valve Lift

k - Turbulent Kinetic Energy (TKE)

L - Characteristic Length

LES - Large Eddy Simulation

m - Mass Flow Rate

n - Time Step

Nu - Nusselt Number

Pr - Prandtl Number

[??]- Wall Heat Flux

R - Radius of Curvature

Re - Reynolds Number

T - Temperature

[T.sub.G] - Gas Temperature

[T.sub.T] - Thermocouple Temperature

[T.sub.W] - Wall Temperature

TDCF - Top Dead Center Firing

u - Velocity

u - Effective Velocity

[u.sup.+] - Dimensionless Velocity

u - Friction Velocity

[y.sup.+] - Dimensionless Wall Distance

a - Heat Transfer Coefficient (HTC)

[R.sub.F] - Convection Factor Thermocouple

y - Heat Transfer Enhancement Factor

[epsilon] - Emissivity

[[theta].sup.+] - Dimensionless Temperature

[lambda] - Thermal Conductivity

[rho] - Density

[sigma] - Boltzmann Constant

[[tau].sub.w] - Wall Shear Stress

[omega] - Specific Turbulent Dissipation

Bjoern Franzke and Stefan Pischinger RWTH Aachen University Philipp Adomeit, Christof Schernus, Johannes Scharf, and Tolga Uhlmann FEV GmbH

Table 1. Technical Specifications of Engines

                   Engine A    Engine B      Engine C      Engine D

Displacement / L    1.0         1.4           2.0           1.2
Bore / mm          73.0        76.0          82.0          77.0
Stroke / mm        78.7        82.6          93.8          85.6
Compression ratio   9.6:1      10.0:1         9.6:1         9.5:1
Number of Valves    4           4             4             4
Exhaust Manifold   integrated  conventional  conventional  integrated

Table 2. Operating Points: Engine Speed (rpm) / BME( MPa) Eng Full Load

Eng             Full Load                        Part      Load

A    1500/2.50  2000/2.50  4000/2.50  5500/2.09  2000/0.2  2500/1.0
B    1600/2.20  2000/2.20  4000/2.20  5500/1.70  2000/0.2  2500/1.0
C    1500/1.85  2000/1.85  4000/1.80  5500/1.66  2000/0.2  2500/1.0
D    1500/2.10  2000/2.15  4000/2.20  5500/1.68  2000/0.2  2500/1.0

Table 3. Nusselt Number Correlation Parameters

Section            1. Phase                  2. Phase

Section 1          0.15 [Re.sup.0715] Pr1/3  0.15 [Re.sup.0686] Pr1/3
Section 2          0.15 [Re.sup.0722] Pr1/3  0.15 [Re.sup.0686] Pr1/3
Runner - straight  0.15 [Re.sup.0693] Pr1/3  0.15 [Re.sup.0663] Pr1/3
Runner - curved    0.15 [Re.sup.0681] Pr1/3  0.15 [Re.sup.0660] pr1/3
Turbine Inlet      0.15 [Re.sup.0701] Pr1/3
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Author:Franzke, Bjoern; Pischinger, Stefan; Adomeit, Philipp; Schernus, Christof; Scharf, Johannes; Uhlmann
Publication:SAE International Journal of Materials and Manufacturing
Article Type:Report
Date:May 1, 2016
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