a turbocharger selection computer model-1999!01!0559

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SAE TECHNICALPAPER SERIES 1999-01-0559

A Turbocharger Selection Computer Model

S. H. NasserDepartment of Aerospace, Civil and Mechanical Engineering

University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK

B. B. Playfoot

Reprinted From: SI Engine Modeling(SP-1451)

International Congress and ExpositionDetroit, Michigan

March 1-4, 1999

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1999-01-0559

A Turbocharger Selection Computer Model

S. H. NasserDepartment of Aerospace, Civil and Mechanical Engineering

University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK

B. B. Playfoot

Copyright 1999 Society of Automotive Engineers, Inc.

ABSTRACT

A variable turbine vane angles turbocharger selectionmodel was developed. The model, which is based on a

single entry fixed vanes angle turbocharger matchingmodel developed in earlier study, is of a modular struc-ture and designed to run on a personal computer. It isbased on the principles of conservation of mass, energyand momentum in one dimension. A heat transfer sub-model was incorporated to account for the exhaust mani-fold losses and to overcome undesirable turbine-inlettemperature profile. Non-isentropic flow was assumedthrough the compressor using one-dimensional, semi-empirical loss calculation formula to improve the predic-tion accuracy of the model at the compressor exit.

The model was verified by comparing the calculated

results with the test data of a Rover 2.4 litter direct injec-tion diesel engine fitted with a 3K-K24 type single entryturbocharger. The engine was coupled to an Eddy-cur-rent dynamometer and provided with facilities to assessits performance under various running conditions. Theverification procedure revealed substantial improvementsin the models accuracy, as compared with the previousmodel, and a more definitive understanding of its limita-tions. The benefit of modeling the heat losses from theexhaust manifold was clearly demonstrated. Comparisonof the predicted and measured results also revealed thatthe model could provide a valuable tool in predicting theperformance of a variable geometry turbocharger. This in

turn confirmed the viability of the improved model andstrongly indicated to its suitability in the initial stages ofturbocharger matching and design.

INTRODUCTION

Rapidly diminishing fossil fuels and increased publicinterest in the impact of their use on the human health,environment, ecology and global climate brought aboutprogressively stringent vehicles emission legislationsince the early sixties (1). More recently, the pressure toreduce CO2 emission has produced the first stage of the

European vehicles emission legislation proposed for theyear 2000 to be closely followed by further legislation in2005 (2). This in turn has increased the pressure todevelop and produce more fuel-efficient engines and

vehicles.

One of the most successful ways of combating harmfuemission and reducing fuel consumption as well asimproving engines, and ultimately the vehicles, performance is by increasing the air available for fuel combustion (3). This can be achieved by fitting the engine with aturbocharger. Although very effective, some characteristics of the turbocharged engines remain unsatisfactoryand matching an engine to a turbocharger to achieve efficient turbocharger operation over a wide range ofengines speed is a difficult and often a compromisingprocess. As an example, matching a large flow turbine to

an engine improves the performance at high enginespeed. However at low engine speed, the exhaust gaspressure will be insufficient to operate the turbine at highenough speed to provide the charge required for full fuecombustion. This can lead to poor combustion resultingin a high specific fuel consumption and poor transienresponse. Consequently, the overall engine performanceis significantly reduced at such speeds. Matching a lowflow turbine to an engine improves the performance alow engine speeds and results in excessively high boospressure at high engine speeds. Bypassing excess gasflow by fitting a waste-gate prevents over-boosting. How-ever, bypassed gases represent energy waste and con-

sequently the turbine operates in a low efficiency rangeAt high speeds, the waste-gate turbocharger is restrictiveto the flow. Consequently, the exhaust manifold pressurebecomes greater than the boost pressure, leading to poocylinder scavenging and high fuel consumption.

To overcome the inadequacy in performance, both thecompressor and turbine flow range capability wereimproved by two methods. On the compressor sidedevelopment of the backswept and raked impelle(depicted in Fig. 1) has been successful in obtaining effi-cient operation over a flow range broad enough toencompass the engine speed range. On the turbine side





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a fix geometry design that achieves efficient operationover a wide enough speed range cannot be achieved,resulting in a compromise between high or low speedperformance. By varying the turbine area, a variablegeometry turbine is an effective way of providing efficientoperation over a wide flow range.

Matching a compressor-turbine combination to an engineis a time consuming and expensive process. Models forcalculating the performance of various turbocharger-

engine configurations enable a close to the optimum tur-bocharger match to be found. Such models are in com-mon use and range from simple mathematicalrepresentation to extremely complicated and costly com-putational flow dynamics, requiring the use of three-dimensional CAD models. The current work expands thefunction of an existing Microsoft Excel based analyticalmodel (4 5) to enable matching of latest generation ofVariable Geometry Turbochargers to direct injection die-sel engine. The accuracy of the fundamental thermody-namics and fluid mechanics concepts employed in themodel are investigated and improved where necessary.In particular, consideration is given to two aspects of the

previous model. The first is the heat transfer through theexhaust manifold. This was assumed to be negligible inthe previous study (4 5). However, a considerableamount of heat loss is reported to occur through theexhaust manifold wall (6 7). Therefore an analysis ispresented to ascertain the change in the turbine inlettemperature due to heat loss with the aim of improvingthe models accuracy. The second is the overall compres-sor isentropic efficiency, which was assigned a certainvalue in the previous study. Hence, the loss in useableenergy due to fluid friction and the rise in aerodynamiclosses at off-design conditions were neglected. This

resulted in an over calculated compressor pressure ratioand was replaced in the current study by a semi-empiri-cal expression accounting for the overall compressorlosses.

THEORITICAL CONSIDERATION

1. THE VARIABLE GEOMETRY COMPRESSOR T h eaddition of vanes to a compressor diffuser enables betterdiffusion by reducing the tangential component of velocitymore rapidly. Consequently, higher pressure-ratio can beachieved. However, the increased blockage increasesthe gas velocity, which in turn lowers the flow capacity

required for choke conditions (when the flow reaches thespeed of sound). At low flow rates the incidence angle ofthe gas at the diffuser blades (due to off-design condi-tions) can have an adverse effect on the surge condition.Employing a variable geometry diffuser enables the inci-dence angle to be eliminated at low flow rates and thethroat blockage minimised at high flow rates. However,compressor designs using non-shrouded impellers arealready available with efficiencies above ninety per cent.The advent of backswept impellers has made the efficientoperating band of a compressor wide enough to copewith the engine operating range. Consequently, the use

of relatively complex and expensive variable geometry isuninteresting for all but the highest performance applica-tions [8, 9].

2. THE VARIABLE GEOMETRY TURBINE The variable nozzle turbine (VNT) has been exploited for manyyears. It consists of a number of guide vanes, equallydistributed around the diffuser ring. By varying bladeangle both the effective turbine area and the rotor inle

gas angle can be controlled.Reducing the turbine flow area at low engine speedsenables the gas flow to be kept high and the turbinespeed fast. This allows more efficient utilisation oexhaust energy than is possible at low speeds with a con-ventional turbocharger. The gas flow is also directed bythe vanes, enabling a greater amount of the tangentiavelocity component to be utilised at low speeds. As aresult, higher boost pressure is available at low speedsimproving torque and reducing smoke. At high enginespeeds, the turbine area opens, to control the gas veloc-ity and prevent over-boosting.

The VNT concept requires a relatively complicated drivemechanism with many intricate components and partsOther variable geometry turbine concepts are sometimespreferred over the VNT concept for their simplicity. However, the VNT has a favorable turndown ratio (ratio ofmaximum to minimum areas) and a more direct controover the tangential gas velocity component and henceturbine torque. The VNT is widely used in the automotiveapplication and, therefore, was chosen as the basicdesign in the current study.

3. ELEMENTARY THEORY OF A VARIABLE NOZZLETURBINE By carrying out a one-dimensional analysis

on the gas flow through the turbine, the torque producedby the turbine and consequently the power to drive thecompressor can be determined. The torque (TQ) produced by the turbine is determined by considering theconservation of angular momentum as follows:

Rate of change of angular momentum = Sum of themoments of the external forces

Angular momentum = Moment of linear momentum

Hence,

(1)

Where denotes the tangential component of velocityand subscripts 4 and 5 denote the rotor inlet and exitrespectively. In the previous study [4-5] the turbine had avaneless diffuser and the tangential component of velocity, C4 was determined by considering the conservationof momentum of the gas between the volute and the rotoinlet. This theory can be expanded to include the effecof the variable nozzle diffuser on the inlet gas flow, asexplained hereafter.

The volute, depicted schematically in Fig. 1(a), guidesthe exhaust gases in an inward spiral pattern to the

)( 5544 CrCrmTQ =





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diffuser inlet. For incompressible flow the continuityequation relates the flow between the volute throat andthe nozzle inlet:

(2)

Where, subscripts 0 and 1 (labelled in Fig. 1b) representthe volute throat and nozzle inlet, respectively. Consider-ing the conservation of angular momentum between thesame points yields the nozzle inlet gas angle:

(3)

Therefore, the nozzle inlet gas angle is a function ofthroat area (A0), the radius of the centroid at the volutethroat (r0), and the nozzle inlet width (b1) as depicted inFig. 1(b).

At the nozzle throat, the total mass flow rate can beexpressed in terms of the throat aperture (LTH2), the noz-zle throat width (b2), the number of rotor blade (z2), and

the gas velocity at the throat (C2).

(4)

Hence, C2 can be found for a given engine speed and tur-bine geometry. The exit gas flow angle (3), depicted inFig. 2, is predicted using common steam turbine theory[10]:

(5)

And

(6)

A vaneless space between the turbine rotor and the dif-fuser blades helps the flow to develop, reduces noise andaids manufacturing. Applying the conservation ofmomentum and continuity equations across the spaceenables the rotor inlet gas angle (4) to be determined:

(7)

Where 3 is the diffuser exit angle in radians, r3 is the dif-fuser exit radius, b4 is the rotor inlet blade width, b2 is thediffuser throat width and z2 is the number of rotor blades.As a result of calculating the rotor inlet gas angle, all theother associated parameters such as turbine speed,power and incidence loss can also be calculated.

4. HEAT LOSSES

4.1 Exhaust manifold heat transfer modeling The thermal inertia of the exhaust system upstream of the turbinemust be taken into account, in order to ensure an opti-mized turbocharger match. The manifold under consideration is a single walled, cast iron construction of theRover 2.4L SD Turbo. Forced convection occurs betweenthe exhaust gas and the pipe wall, followed by heat con

duction through the wall to the connecting surfaces. Inthe stationary test bed environment, natural convectionoccurs between the outer surface and the surroundingatmosphere. Radiation from the pipe surface alsobecomes significant at surface temperatures above 400oC. Proper modeling of the overall heat transfer results ina precise prediction of the turbine inlet temperature andhence, enables an accurate assessment of the effects othe manifold geometry and material on the turbochargeperformance. In the following steady-state analysis, anaverage exhaust gas mass flow rate is employed.

4.2 Component interior heat transfer The exhaust gas

flow through the manifold is often lower than that requiredfor the laminar turbulent transition (Re = 2300). How-ever, the flow is always turbulent due to the constanrestriction of the exhaust valve and the unsteady flow pulsation effects of the reciprocating engine. Consequentlythe effect of forced convection is considerably greatethan might be expected for such flow. The heat transferdue to forced convection is related to the heat transfecoefficient, as follows: -

(8)

Where hcv,i denotes the internal heat transfer coefficien

due to convection, Ai is the internal surface area and Tlnis the logarithmic mean temperature difference. Thismeasure of temperature difference assumes that theinternal surface is at constant temperature and the temperature difference decays exponentially in the flow direc-tion.

The convective heat transfer coefficient, hcv, is determined from the Nusselt number, Nu, with the followingrelationship:

(9)

Where di represents the internal diameter and ki, theaverage exhaust gases thermal conductivity. Numerousequations have been developed using experimental cor-relation, that express the Nusselt number as a function ofReynolds number (Re) and Prandtls number (Pr). Theaccuracy of the relationships varies from application toapplication depending on the assumptions made. Byaveraging the dimensions of each runner, the manifold

1100 CACAV ==

=

10

01

12

cotbr

A

22222 zLbCm TH=

=

3

21

3 cosSp

LTH

=3

3A

mC

=

3222

431

4 sin

2

tan

zLb

br

TH

ln, TAhQ iicv =

=

i

ii

i

k

dhNu





6/204

can be modelled by a single representative runner. As aresult, the model consists of a bend from the exhaustport, leading to a straight pipe followed by a final bend tothe turbine interface. Modelling the manifold in this wayenables the proximity of the exhaust valve to be included.The model can also be altered to suit different manifoldswithout requiring too much information.

For steady flow in a straight, circular pipe the interiorNusselt number can be calculated from the Seider-Tate

relationship, [12-13]:

(10)

Initially, an internal surface temperature must beassumed in order to determine the film temperature atwhich the exhaust gas properties (such as Re, Pr, CP, ,, etc.) are calculated.

The temperature difference between the centre line gasand the wall is usually greater than 100C. Equation (10)should therefore be factored by the following relationshipto take into account for differences in dynamic viscosity:

(11)

Where bulk and skin are the gas dynamic viscosity atthe bulk gas and pipe surface temperatures, respectively.Badly separated flow at the manifold inlet results from theentrance effect of the exhaust valve. A factor, whichtakes into account the separation effect, is defined as fol-lows:

(12)

Where L, is the entrance length. Hence, the product ofequations 10-12 can be used to calculate the total idealflow interior Nusselt number:

(13)

The effect of a bend is determined by factoring the Nus-selt number of an equivalent straight pipe to take intoaccount the increased turbulence at the bend:

(14)

The turbulent boundary layer inside the manifold are notfully developed because of pulsation in the exhaust pres-sure and the effect of wall curvature. Consequently, theNusselt number is observed to be considerably higherthan the ideal-flow prediction. The Convective Augmenta-tion Factor (CAF) is used to quantify this increase [12-13]. CAF values between 2.5 & 3.0 are appropriate for

the exhaust manifold [12]; more exact value can beobtained by experimentation. The convective augmentation factor is defined as:

(15

Considerable heat loss occurs as the exhaust gaspasses through the cylinder head. This is caused mainly

by (a) water cooling in the cylinder head and (b) highlyturbulent flow in close proximity to the exhaust valves. Noconclusive information has been found regarding thiscomponent of heat loss. However, the loss is largelydependent on the gas mass flow rate and it is therefore areasonable factorise the overall heat transfer.

4.3 Component Exterior Heat Transfer For sta tionar yapplications such as the engine test bed, the exter-nal convection is natural. The Nusselt number isexpressed by the following equation:

(16

The Rayleigh number, Ra, is determined by:

(17)

Where:

= Characteristic length (pipe diameter), m

g = Gravitational acceleration, m/s2

= Coefficient of volume expansion for the ambienair, 1/K

= Kinematic Viscosity, m2/s

The external heat transfer coefficient, hcv,o, can thereforebe obtained using the relationship described in equation9.

Convection and radiation occur simultaneously at theouter surface. Assuming a reasonable ambient air temperature, the radiation heat transfer coefficient, hrad,canbe expressed as:

(18)

Where;

= Radiation emissivity factors= Stefan-Boltzmann constant, W/m2K4

The outside surface temperature, Ts,o, is initially calculated using standard pipe conduction theory and theapproximated internal pipe surface temperature.

3/18.0

,PrRe027.0=steadyiNu

14.0

=

skin

bulkviscC

i

entr dLC /

02.2

892.0.0 +=

entrviscsteadyiideal CCNuNu ..,=

CAFNu

Nu

effective

theoretical

=

[ ]Nu

Rao

amb= ++

0 75

0387

1 559

1 6

9 168 27

2

.. .

(0. / Pr)

/

//

Rag T T

amb

amb s o o=

3

2

. . .( ).Pr, ,

h T T T T rad s o s o= + + . .( )( ), ,2 2





7/205

5. EXHAUST MANIFOLD EXIT TEMPERATURE Assuming the temperatures of the internal surface, exter-nal surface and surrounding air are constant along themanifold length, the exit gas temperature (Te) can bedetermined by:

(19)

Where Ts is the internal surface temperature, Tin is the

manifold inlet temperature, and L represents the meansection length. The total heat transfer coefficient is repre-sented by Uand is defined by Equation 20:

(20)

Using equations 920, the turbine inlet temperature canbe determined. The total heat loss can then be deter-mined by the Equation 21:

(21)

Using equation (8), an improved approximation of theinternal surface temperature can be obtained. Employingthis iterative process, a complete steady state modelincorporating all the heat transfer components is pro-duced.

6. NON-ISENTROPIC FLOW THROUGH THE RADIALFLOW COMPRESSOR The flow through the centrifu-gal compressor is highly turbulent and three-dimensional.Consequently, the loss modelled using one-dimensionalanalysis is very reliant upon experimental data. Energylosses within the compressor stage can be broadly

divided into aerodynamic loss, disc friction loss, leakageloss and mechanical losses.

6.1 Inlet Casing Losses In an automotive turbochargerwith inboard bearings, the pressure loss through the airfilter is far greater than that occurring in the inlet casing.Consequently, the small aerodynamic losses that arepresent during this stage can be neglected [10].

6.2 Impeller Losses The impeller, depicted in Fig. 3,imparts a swirling motion on the air, which leaves theimpeller tip at high velocity. Work transfer takes place inthe impeller and the static pressure of the air increasesfrom the inducer to the impeller tip due to centripetalacceleration and diffusion. Watson and Janota [10]divided the losses in the impeller into:

(i) Fluid friction losses.

(ii) Diffusion and blade loading losses due to bound-ary layer growth, separation and mixing.

(iii) Blade incidence loss due to off-design angles ofthe inlet gas at the inducer.

(iv) Re-circulation losses due to clearance, facilitatedby; (a) flow across the tip of the impeller from thepressure side to the suction side and (b) thebackflow of air along the shroud from the impelletip to the inducer.

(v) Disc friction losses due to the shearing of aibetween the back face of the impeller and thestationary housing.

(vi) Shock losses, associated with sonic flow at the

inducer entry under high-pressure ratio opera-tion.

Cumpsty [14] suggested that the losses in good impellerscannot be very high because the efficiencies close to theoptimum specific speed are very high. For non-shroudedimpellers with an inducer, isentropic efficiencies as highas 93 per cent are attainable. This is possible sincemuch or even most of the static pressure rise comes fromthe centripetal force imparted on the air, which is inde-pendent of fluid losses and depends only on the impellerblade speed at inlet and outlet. Diffusion in the impellepassage contributes the remaining static pressure rise

and depends on fluid flow. This free static pressure risedue to centripetal effects is very fortunate because thenarrow flow path through the impeller channel is veryconducive to high losses.

6.2.1 Fluid friction losses Application of the energy andmomentum equations to pipe flow with surface frictionshows that the energy loss, due to surface friction in theimpeller channels [9,15], can be calculated:

(22

Or

(23

Where:

Ch = Surface friction loss coefficient

f = Friction factor

L = Mean channel length, m

D = Mean hydraulic channel diameter, m

W = Mean relative velocity at inlet, m/s

The surface friction loss coefficient, Ch, is an empiricaconstant that contains a factor for blade loading and diffusion losses as well as for surface friction. This is possiblesince the pressure ratios common in most automotive turbochargers are not enough to make blade loading anddiffusion losses dominant. An advantage of this methodis that it does not imply an accurate knowledge of thecomponent losses in the impeller, which are impossible toseparate experimentally.

).(..).( p

CmLU

insse eTTTT=

oradocv

io

ii dhhK

rr

dhU ).(

1

.2

)/ln(

.

11

, +++=

)(. einP TTCmQ =

24

42

1W

D

Lf

D

lh ==

h ChL

D

W= 1

2

2





8/206

6.2.2 Blade incidence loss Blade incidence loss, alsotermed shock loss, takes into account the flow separa-tion caused by off-design inlet gas angles at the impellereye. Consequently, the loss at the design speed is zeroand the further away from the design speed, the greaterthe angle of incidence and therefore the greater the loss.It is assumed that the fluid approaching the impellerblade instantaneously changes direction, from 1 to 1b ,to comply with the blade angle, as can be seen in Fig. 4.

Ca1 is the incoming gas, which is assumed to be perpen-dicular to the impeller eye (no pre-whirl). W1 is the veloc-ity of the incoming gas relative to the impeller eye tipvelocity, U1. As depicted in Fig. 4, W1 can be resolvedinto a component W1b in the direction of the impellervane (1b) and a component W1 in a direction tangentialto the impeller eye. A simple loss model is to assumethat the kinetic energy associated with the tangentialcomponent, W1, must be destroyed when the gasinstantaneously changes direction. Hence, the energyloss due to incidence is given by Equation 24:

(24)

It is important to note that the term shock loss is mis-leading since nothing akin to shock occurs in practice.The term originates from the approximation abovebecause the fluid approaching the inducer blade isassumed to experience an instantaneous change ofvelocity.

6.2.3 Re-circulation Losses Re-circulation losses arenormally caused by two mechanisms. The first is the flowof air along the shroud from the impeller tip to theinducer, due to tip clearance as depicted in Fig.5. The

second is the backflow of air across the blade tip from thepressure side of the vanes to the suction side.

Several methods of predicting the loss in efficiency due totip clearance have been developed using experimentaldata. The effect is conventionally expressed as a loss inefficiency, /. According to Cumpsty, [14] remarkablygood predictions of tip clearance loss for a number ofcompressors have been produced using a very simplemodel developed by Senoo and Ishida in 1987. Thereduction in efficiency was found almost proportional tothe ratio of clearance-to-blade height at the impeller out-let, provided the ratio is less than 0.1. The relationship is

expressed in Equation 25:

(25)

Where:

t = axial blade tip clearance

bl = blade height at impeller outlet

A small amount of clearance can actually increase theoverall efficiency of the impeller stage. This is because a

small clearance flow alters the main flow in such a waythat the overall flow is improved [10].

Controlling the clearance in automotive turbochargercompressors is extremely difficult and large clearancesare common due to the requirement for long life at veryhigh rotational speeds. Consequently, the efficiency osuch compressors is likely to drop by several per centdue to tip clearance losses.

The impeller back flow loss is a result of the work inputrequired to re-process fluid that has been re-injected intothe impeller due to pressure gradients existing at theimpeller tip. The loss depends on the impeller exit Machnumber, exit swirl and the number and proximity of dif-fuser vanes to the impeller tip. No mathematical modecurrently exists that fully describes the back flow losswhich should be considered as another aerodynamicdesign parameter. However, an empirical correlation foback flow loss was developed by Coppage et al, as follow[10]:

(26

Where:

C2 = Tangential velocity at the impeller exit, m/s

Cr2 = Radial velocity at the impeller exit, m/s

Df = Diffusion factor

U2 = Tangential velocity at the impeller tip m/s

6.2.4 Disc Friction Losses When a disc is rotated in afluid there is a resistive torque generated by the tangential shear component between the disc and the fluid. Anestimation of the power input necessary to overcome thefriction at the external surfaces of the impeller can bemade from research considering the resistive power ofplane discs enclosed in casings. The resulting relationship is defined as follows:

(27)

Where Cm is a non-dimensional torque coefficienobtained from experimentation and is a function of thedisc Reynolds number and the disc-casing spacing ratio(s/r2) depicted in Figure 5. Ferguson [15] presentedresults correlating the variation of the torque coefficien

with Reynolds number and the disc-spacing ratio forsmooth discs.

6.2.5 Shock Losses The diffusion processes in theimpeller are related to the flow mach number. It is desirable to establish conditions that lead to a minimum rela-tive mach number at the impeller inlet and a minimumabsolute mach number at the impeller outlet in order toachieve maximum diffusion.

The tip of the inducer eye is the point where the highestrelative Mach number occurs. Careful consideration

hW= 1

2

2

1

4

t

bl

= 0 02 2 21 2 2

2

2. ( / )

/C C Df U r

2

).(5

1

5

2

3rrCm

W

=





9/207

should therefore be made on the diameter of the inducereye. A method of determining the inducer eye diameterat which the minimum relative mach number occurs wasdiscussed by Adams in the previous study [16].

When the flow velocity reaches the speed of sound atsome cross section, the flow chokes. For a stationarypassage, such as the diffuser, this means that no furtherincrease in mass flow through the compressor is possi-ble. The speed in the rotating impeller channels is rela-

tive to the blade speed. Consequently, as the impellerspeed increases, the compressor can accept a greatermass flow before choking, unless choking occurs in a sta-tionary area.

6.3 Vaneless Diffuser The air leaves the impeller tip ata high absolute velocity and normally at a large inclinedangle to the radial direction. In order that the pressurerise and efficiency of the compressor are acceptable, thediffuser must decelerate the flow.

The diffuser must cope with the highly turbulent flow fromthe impeller. The combination of three dimensional

boundary layers and unsteady inlet flow makes the flowthrough the diffuser extremely difficult to predict. By con-sidering one-dimensional viscous flow, an estimation ofthe friction losses can be made to help the engineer atthe preliminary design stage. Japikse (1984) recom-mended the following expression for use with one-dimen-sional analysis, where Cfis the coefficient of friction andKis an empirical constant.

(28)

The value of Kvaries between 0.025 and 0.0074, indicat-ing the inaccuracy or incompleteness of the equation. By

considering the effective hydraulic diameter of the dif-fuser an expression for enthalpy loss can be derivedusing non-circular duct theory. Hence,

(29)

Where

f = Friction factor (= 4Cf)

l = Diffuser length, m

C4= Mean velocity, m/s

y = Mean wetted perimeter, m

A = Mean flow area of diffuser, m2

6.4 Volute Down-stream of the diffuser is the Volute (orscroll), that collects the flow and decelerates it further.By considering the continuity equation and conservationof angular momentum, the volute can be designed sothat there is no incidence between the gas flow angle andthe angle of the volute [10,17]. However, at mass flowrates other than those at the design conditions, an angleof incidence will exist causing quite serious effects on the

flow in the impeller and vaneless diffuser [10]. The result-ing non-uniformity of flow may be evident upstream of theimpeller and because of this; compressors often surge ata higher flow rate than under uniform flow conditions. Theflow in the volute is slow enough that friction is not likelyto have a major effect. Most of the loss comes from thekinetic energy associated with the radial velocity (cr5)being destroyed as the flow is constricted by the volutewall.

According to Cumpsty (10), better efficiency can beachieved by reducing the volute area by 10 to 15 per cenof that suggested by the conservation of angular momentum. This results in the radial flow component beingturned towards the circumferential direction by creating agradient in static pressure along the volute length. However, the resulting non-uniformity of flow in the volute disturbs the flow throughout the entire compressor makingthe losses extremely difficult to predict. The actual workrequired to drive the compressor can therefore be calculated, and the corresponding compressor efficiencydetermined.

MODEL DEVELOPMENT

Three new modules have been added to the originaExcel based model to facilitate:

Nozzle exit gas angle calculation in the Variable Nozzle Turbine.

Heat loss calculations in the exhaust manifold.

Compressor loss calculation.

The integration of the modules and their interaction withthe other components can be seen in Figure 6.

Modules 1, 2 and 3 are the core components and arealmost unchanged from the previous model. Modules 4to 6 contain the theory explained in previous sections. Ascan be seen from the Figure 6, there are four main loopsin the model where data is iterated. Equations in the iterative loops are linked using circular references so that nomanual iteration is necessary. Equations tend to crash ione of its input values changes too much between itera-tions. To ensure numerical stability, a method of control-ling the rate at which a value converges has beenintroduced.

(30)

Where subscripts 1 and 2 denote 1st and 2nd iterationsrespectively and K is a factor that controls the speed oconvergence. As a result of introducing Equation (30)the model is completely stable, with no maximum enginespeed limit. A separate module was added to the modespecifically for data acquisition and contains simple logiccommands that record all the major parameters for theentire engine speed range.

Cf K= ( . / Re)18 105 0.2

hflc y

A=

3

4

4

2

KValuesofMedian

valuesiterationinDiff..

21

+= ValVal





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RESULTS

MODEL CHARACTERISTICS

1. Variable Nozzle Turbine The effect of changing thenozzle angle and the control the turbine effective flowarea on the compressor boost pressure ratio (termedarbitrarily as P2/P1) is clearly shown in Figure 7. The abil-ity of variable geometry to limit boost at high engine

speeds and maximise boost at low speeds is clearly evi-dent.

2. Manifold Heat Transfer In order to provide a directcomparison with the results of the previous model, fixedturbine geometry was considered in the calculation ofboth the heat transfer and compressor losses. Figure 8shows the change in the exhaust manifold heat transferwith the mass flow parameter (MFP). The MFP was cal-culated from gas flow rate normalised by the turbine inletarea, exhaust gas specific heat at constant pressure andexhaust gas stagnation pressure and temperature. It cor-responds to an engine speed range of 1000 to 6000 rev/

min. The increase in the overall heat transfer with MFPwas predominantly caused by an increase in the internalheat transfer coefficient. This, in turn, was a direct conse-quence of higher turbulence level in the exhaust gas gen-erated mainly by higher gas mass flow. The contributionof the radiation losses to the overall heat transfer alsoincreased marginally, due to the increase in the manifoldsurface temperature.

3. Compressor Losses The variation in the impellerchannel friction loss with the compressor mass fractionparameter (MFP) is shown in Figure 9. The compressorMFP was calculated from the gas mass flow rate norma-

lised by the appropriate parameters at the inlet condi-tions. As can be seen, the surface friction loss coefficient(Ch) has a considerable effect on the channel frictionloss. Unfortunately, no material in the literature has beenfound that suggests suitable values for this coefficient. Acoefficient such as this must be employed because noone-dimensional technique is available to analyse thelosses associated with the coefficient.

Minimum incidence angle loss can be achieved by con-sidering the inducer eye blade angle at the design stage.Figure 10 shows the loss for an impeller designed formaximum efficiency at 4000 rev/min. The remaining loss

components follow simple exponential and linear relation-ships as was shown in the relevant equations. Thechange in the total compressor efficiency with the massflow parameter is shown in Figure 11. Despite the consid-eration of the design speed it would appear that the opti-mum efficiency occurs at the maximum speed.Unfortunately, this can not be the case since there is con-siderable fluid friction and offdesign aerodynamic lossesat high speeds. The impeller geometry is also optimisedfor the mid engine speed range [16].

MODEL ACCURACY

1. Variable geometry turbine In order to determine thepredictive accuracy of the variable geometry, turbinecharacteristic charts are required indicating the change inexpansion ratio with turbine speed for various nozzle settings. Such material is available but no dimensional information is included. A non-dimensional analysis is noappropriate because dimensions such as nozzle angle

width and length determine the turbine characteristicsConsequently, no direct comparison has been maderegarding the accuracy of the variable geometry withinthis paper. However, the qualitative nature of Figure 7 isencouraging.

2. Heat transfer Comparison of the predicted resultsfrom the current model with experimental data and analytical results of the old model (16) is depicted in Figures12-14. The increase in the prediction accuracy of the turbine inlet temperature of the current model is clearlydemonstrated in Figure 12.

3. Compressor Losses Many of the relationships areaccurate when applied at the design speed; however, theflow at off-design conditions becomes considerably morecomplex. Turbulence created in one part of the compressor effects the flow down-stream and this has not beentaken into account in the model. The flow at the inlet tothe diffuser from the impeller tip is highly unsteady andnon-uniform. Furthermore, at high-pressure ratios theflow will be highly swirling, turbulent and boundary layerseparation will be significant. This complex and highlythree-dimensional flow cannot be accurately modelledusing one-dimensional analysis. Consequently, the cur-rent model is useful for initial design purposes but is

potentially misleading for detailed flow analysis.

As Figure 15 shows, the compressor pressure ratio pre-diction, is considerably less accurate when using one-dimensional loss analysis. The values rapidly divergetowards the higher engine speeds. This would appear tobe caused by the losses in the compressor build up faquicker than predicted by the model. This would alsoexplain the compressor efficiency result depicted in Figure 11. At high engine speeds, the poor pressure ratioprediction severely effects the manifold temperature calculation. Mass flow rates, fuel consumption and enginepower are all related to the induction pressure and are

therefore also detrimentally effected.

CONCLUSIONS

(i) An existing Excel based analytical model hasbeen improved to facilitate comparative perfor-mance predictions of a Variable Nozzle turbineNo direct comparison of the variable geometryturbine predictive accuracy has been made dueto a lack in supportive data.





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(ii) The addition of a manifold heat transfer analysishas reduced the maximum turbine inlet tempera-ture calculation error from 63% to 14%. A fur-ther improvement could be obtained by adding amore extensive combustion analysis to the pro-gram.

(iii) The flow through the compressor is highly com-plex and three-dimensional. This study hasshown that a one-dimensional, empirically based

loss analysis cannot provide the accuracyrequired. An increase in the pressure ratio pre-diction error from 10% to 24% was observed.

(iv) The model enables comparative performancepredictions for different Variable Geometry Tur-bocharger configurations. The effect of turbinenozzle position on performance can be predictedenabling a preliminary control strategy to beestablished before testing commences.

(v) The previous model enabled the effect of com-pressor and turbine geometry to be established,allowing the optimum configuration to be deter-

mined. By considering heat loss through theexhaust manifold the accuracy of these predic-tions is considerably improved.

REFERENCES

1. Degobert, P., Automobile and Pollution, SAE publications,

1995.

2. OECD, Motor vehicle pollution; reduction strategies

beyond 2010, 1995.

3. SAE, Emission processes and control technologies in die-

sel engines, 1995.

4. Nasser, S. H. and Adams, P. W., A simple analytical/math-ematical model for turbocharger matching, Paper No.

96VR017, 29th ISATA Conference on Simulation/Diagnosis

and Virtual Reality in the Automotive Industry, Florence,

Italy, June 1996.

5. Nasser, S. H. and Adams, P. W., A Simple mathematical

model for turbo-charger matching, 1st ATA International

Conference on Control and Diagnostics in Automotive

Applications, Genoa, Italy, October 1996.

6. Wendland, W. D., Automobile exhaust-system steady state

heat transfer, SAE 931085, 1993.

7. Konstantinidis, P. A., Koltsakis, G. C. and Stamatelos, A.

M., Transient heat transfer modelling in automotiveexhaust systems, C11395, 1997.

8. Okazaki, Y., Matsudaira, N. and Hishikawa, A., A case of

variable geometry turbocharger development, Proceed-

ings of the Institution of Mechanical Engineers 1986-4,

(C111/86), 1986.

9. Watson, N., Turbocharging Developments on Vehicle Die-

sel Engines, SAE 850315, 1985.

10. Watson, N. and Janota, M. S. Turbocharging the internal

combustion engine, MacMillan, 1982.

11. Watson, N. and Banisoleiman, K., A variable-geometr

turbocharger control system for high output diese

engines, SAE 880118, 1988.

12. Wendland, W. D., Automobile exhaust system steady stat

heat transfer, SAE 931085,1993.

13. Konstantinidis, P. A., Koltsakis, G. C., and Stamatelos, A

M., Transient heat transfer modeling in automotive exhaus

systems, C11395, 1997.

14. Cumpsty, N. A., Compressor aerodynamics, Longma

Scientific & Technical, 1989.

15. Ferguson, T. B., The centrifugal compressor stage, Bu

terworths, 1963.

16. Adams, P. W., Turbocharger matching technique on diese

engine, Project report, Department of Aerospace, Civ

and Mechanical Engineering, University of Hertfordshire

1995.

17. Dixon, S, L., Fluid mechanics, thermodynamics of turbo

machinary, 1966.

NOMENCLATURE

Symbols and units

A: Surface area (m2)b: Diffuser width (m)bl: Impeller blade width (m)C: Velocity (m/s)Ch: Surface friction loss coefficientCm: Torque CoefficientCP: Specific heat (kJ/(kg.K))D: Mean hydraulic diameter (m)d: Diameter (m)Df: Diffusion factorf: Friction factorg: Gravitational acceleration (m/s2)h: Heat transfer coefficient (W/(m2.K))i: Incidence angle (radians)K: Empirical constantk: Conductivity (W/(m.K))L: Length (m)LTH: Throat aperture (m)

: Mass flow rate (kg/s)MFP: Mass flow parameterPr: Prandtl numberr: Radius (m)Ra: Rayleigh number

Re: Reynolds numberSP3: Blade pitch (m)t: Blade tip clearance (m)U: Blade tip velocity (m/s)U: Heat transfer Coefficient (W/(m2.K))

: Volumetric flow rate (m3/s)

: Power (kW)W: Relative velocity (m/s)x: Length (m)y: Wetted perimeter (m)z: Number of rotor blades

m

V

W





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: Kinematics viscosity (m2/s): Gas angle (radians)

Thermal expansion coefficient (1/K)

: Characteristic length (m): Increment: Emisivity factor: Efficiency: Dynamic viscosity (kg/(m.s))

: Density (kg/m

3

)Stefan-Boltzmann constant

: Shear stress (N/m2): Angular velocity (radian/s)

Subscripts

0 : Volute Throat1 : Nozzle Inlet, impeller eye2 : Nozzle Throat, compressor impeller exit3 : Nozzle Exit, compressor diffuser inlet

4 : Rotor Inlet, compressor volute5 : Rotor Exita: axialb: Gas flow angle in direction of bladeamb: ambientbulk: Conditions at bulk gas temperaturecv: convectione: Manifold exiti: inner

in: manifold inletln: logarithmic meano: outerr: radialrad: Radiations: Manifold surfaceskin: Conditions at manifold skin temperaturesteady: Steady state

Free stream conditions

: Tangential

Figure 1a. Schematic diagram of the Variable Nozzle Turbine (VNT) concept





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Figure 1b. Turbine volute geometry

Figure 2. Determination of the nozzle exit gas angle





14/2012

Figure 3. Impeller detail

Figure 4. Velocity change concept in shock loss theory





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Figure 5. Disc friction notation

Figure 6. Layout and interaction of modules





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Figure 7. The effect of nozzle angle on the compressor pressure ratio

Figure 8. The relationship between manifold heat loss and the exhaust gas mass flow parameter





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Figure 9. Change in impeller channel friction loss with engine speed and friction loss coefficient

Figure 10. Inducer blade incident loss





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Figure 11. Change in total compressor efficiency

Figure 12. Improvement in turbine inlet temperature achieved by the heat losses modelling





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Figure 13. Improved expansion ratio prediction

Figure 14. Improved turbo speed prediction





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Figure 15. Poor pressure ratio prediction of new model due to inaccurate compressor loss prediction away from designconditions




a turbocharger selection computer model-1999!01!0559

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