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CFD Modeling for theEstimation of PressureLoss Coefficients of PipeFittings: An UndergraduateProjectKUMAR PERUMAL,1 RAJAMOHAN GANESAN2

1Department of Chemical Engineering, Curtin University, Miri, Sarawak, Malaysia

2Department of Mechanical Engineering, Curtin University, Miri, Sarawak, Malaysia

Received 2 January 2015; accepted 9 August 2015

ABSTRACT: This work reports the outcomes of a senior undergraduate project done as part of a CFD courseoffered at Curtin University, Malaysia. Pressure loss coefficients for single phase flow through 90 degree bend has

been estimated using CFD simulation. It is evident from the results that a validated CFD model is a reliable and

cheap tool forloss coefficient estimation of anycombinationof pipe fittingand complex fluid / flow. 2015 Wiley

Periodicals, Inc. Comput Appl Eng Educ 24:180185, 2016; View this article online at wileyonlinelibrary.com/journal/

cae; DOI 10.1002/cae.21695

Keywords: 90 degree bend; CFD; multiphase flow; pressure loss coefficient

INTRODUCTION

Pipe ttings such as valve, bend, tee, elbow, contraction and

expansion are integral part any piping system found in chemical

and allied industrial processes. These are mainly used to control

the ow rate and change thedirectionofow, which causes energy

loss in addition to that caused by the uid ow through straight

pipes. Flow ofuids in a piping system is accompanied by both

skin and form friction, resulting in pressure or energy loss. Skin

friction, which is responsiblefor pressure lossin straightpipe ow,

is the friction between the pipe wall and the uid and also between

the uid layers. Whereas, form friction is caused by pipettings as

the uid is subjected to sudden velocity and direction changes.

Reliable pressure loss coefcients for various pipe ttings are

needed to calculate the additional energy loss and determine the

correct pump size [1]. The classic reference for such data is the

Chemical Engineers handbook [2]. Butthis data arelimited to only

single phase ow of Newtonian uids. Industrial ows are often

complex involving either multi phases (i.e., solidliquid, gas

liquidsolid) or non-Newtonian uids. The pressure loss

coefcients for such uids and ows are not readily available in

hand books. So there are several attempts by researchers to

determine these coefcients. In one of the earliest works, Griskey

and Green [3] determined pressure loss coefcient data for dilatant

uids. Turian et al.[4] provided loss coefcients for turbulentows

of concentrated non-Newtonian slurries and Telis-Romero et al. [5]

presented the data for laminarow of pseudo plastic uids.

The summary of the published literature is given in Table 1.

A careful examination of the literature reveals that most of the

previous work is experimental (E) in nature, which is expensive

compared to the numerical simulation (CFD) studies. The cost of

experimental studies further increases when it involves sophisti-

cated instruments such as Electrical Capacitance Tomography,

Wire Mesh Sensor Tomography. Because of the low cost, use of

CFD for the study ofuid mechanics, heat and mass transfer of

various chemical processes has increased signicantly in the last

decade or so.

Computational Fluid Dynamic (CFD) simulations predict

ow variables such as velocity, pressure ect, by solving the

mathematical equations describing the relationship between the

ow variables. So the accuracy of the simulation results depends

on how well the mathematical model or equations captures the

ow physics. Theaccuracy of the mathematical model is evaluated

by comparing the simulation results with the experimental results.

This process is called validation in CFD parlance. The

Correspondence to K. Perumal (p.kumar@curtin.edu.my).

2015 Wiley Periodicals, Inc.

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Table 1 Summary of Published Literature on Pipe Fittings

Reference Pipe fitting Fluid Remarks

Gardner and Neller

[6]

908 bend Air water (E), One of the early works in which flow distribution in

bend was measured experimentally

Carver [7] 908 bend Air water (CFD), The two dimensional model results did not match

well with the experimental results of Gardner and Neller

[12]

Michaelides and Lai

[8]

Return bend Air solid (E), Comparison between experimental and correlation

predicted pressure drop is good

Hilgenstock and

Ernst [9]

908 bend Single phase (CFD), It is suggested that CFD should be used in

conjunction with experiments to understand three

dimensional flow field

Legius and Van der

Akker [10]

908 bend Air water (E & CFD), Good agreement between modelling and

experiment results has been found

Pal and Hwang [11] Globe valve, sudden contraction

and sudden expansion

Oil in water

measured emulsion

(E), Pressure loss coefficients are as function of Reynolds

number covering laminar and turbulent regimes

Venkatasubramanian

et al. [12]

Bends Coalair (E), Among the tested bends, (Long radius, Short radius and

Blinded T bend), Blinded T was found to be best for

pneumatic transport of coal

Deshpande and

Barigou [13]

Sudden contraction and

sudden expansion

Gasliquid (E), Presence of pipe fittings in foam flow is found to affect

the foam structure seriously. This may have foam serious

practical implications when preservation of foam structure

is important

Deshpande and

Barigou [14]

Bend, elbow, orifice plate and

perforated plate

Gasliquid foam (E), Except orifice plate, all other fittings (bend, elbow,

perforated plate) introduce large differences in liquid

holdup and pressure drop gradient between the flows in the

upstream and downstream pipe sections.

Polizelli et al. [15] Butterfly valve, plug valve,

Bend and union

Xanthan gum (E), Pressure loss coefficients were determined and

correlated in terms of Reynolds number

Fester et al. [16] Diaphragm valve Water, glycerol

and CMC

(E), Pressure loss coefficients are measured in the laminar,

transitional and turbulent regimes for valves ranging from

40 100 mm

Spedding and

Bernard [17]

908 Elbow Gasliquid (E), A general correlation was presented for the elbow bend

pressure drop in terms of Reynolds numbers

Spedding et al. [18] 908 Elbow Water oil air Three phase flow is more complex than the two phase flow

Fester and Slatter

[19]

Globe valve Water, glycerol

and CMC

(E), Correlation for pressure loss coefficients was developed

for fully and half open positions

Liu and Dian [20] 908 bend, gradual and sudden

contraction

Coal water slurry (E), It is observed that each fitting has a significant and

different pressure loss

Abdulkadir et al. [21] 900 bend Airsilicone oil (E), Flow pattern has been studied using advanced

instrumentation such as Electrical Capacitance

Tomography and Wire Mesh Sensor Tomography

Cabral et al. [22] Butterfly valve, Ball valve, Bend,

Tee and Union

Liquid food products (E), Pressure loss coefficients are measured as function of

generalized Reynolds number covering laminar and

turbulent regimes

Kotze et al. [23] Diaphragm valve CMC (E), Velocity profiles are measured using ultrasonic velocity

profiling technique

Sharma et al. [24] Rectangular and U Return Bend Oilwater (E), Due to the sharp changes in flow direction, the

rectangular bend has a higher value of bend pressure drop

Kaushik et al. [25] Sudden contraction and sudden

expansion

Oilwater (CFD), A detailed study has been performed to generate

profiles of velocity, pressure and volume fraction of phases

over a wide range of water and oil velocities

Ma and Zhang [26] Tee, sudden contraction, sudden

expansion and 908 elbow

Phase change slurry (E), Correlations for pressure loss coefficients are developed

using the experimental data

Alimonti et al. [27] Gate and Globe valve Gasliquid (E) Valve coefficients are determined as function of valve

openings

Joyce and Soliman

[28]

Tee junction Air water (E) two-phase pressure drop through a horizontal, equal-

sided, sharpedged, combining tee junction was measured

and the new experimental data were used to assess the

performance of existing models

Nan Lin et al. [29] Elbow Gassolid (CFD) Effect of gas and solid velocity on erosion of elbows

studied

Saidj et al. [30] 908 bend Air water (E) Conductance probe technique has been used to study the

flow pattern upstream and downstream of bend

Vieira et al. [31] 908 bend Gasliquid (E) Dual wire mesh sensor has been used to study the effect

of bend on the stratified and annular flow characteristics

CFD MODELING FOR THE ESTIMATION OF PRESSURE LOSS 181

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mathematical model is renedtill a reasonable agreement between

the simulation and experimental results is attained. Such a

validated model can be used with condence to get a deeper

insight of the underlying physical mechanisms and to predict

velocity and phase distribution with high spatial and temporal

resolution for complex industrial ows [32]. Similar experimental

studies of such ows are expensive as sophisticated instrumenta-

tion is needed. Thus, CFD technology is an effective and versatiletool forow predictions if the physical phenomena are adequately

described by the mathematical model. It should be mentioned here

that experimental studies are indispensable to get the mathemati-

cal model validated.

Recently, Computational Fluid Dynamics (CFD) simulation

is increasingly being used as a teaching and research tool in the

undergraduate Mechanical, Chemical and Food Engineering

courses [3337]. It is either taught as a separate course or used

in courses like Fluid Mechanics and Heat Transfer to enhance the

teaching and learning process. It must be noted that CFD is taught

mostly as an elective course in many universities around the world

[34]. It is believed that CFD must be made a core part of the

undergraduate curriculum as it is widely used in the industry and

academia as a design and optimization tool [3437]. As a teaching

aid, CFD can make Transport Phenomena education interesting as

it allows visualization ofow, temperature, pressure and species

elds [35].

The objective of this work is to demonstrate the use of CFD

simulation for the determination of pressure loss coefcients. This

has been done for single phase Newtonian uid ow through a 90

degree bend. A good agreement between the simulated and

empirical loss coefcients gives credibility to CFD simulation for

its application to multiphase ow predictions.

CFD MODELING

Geometry Creation and Grid Independence StudyGeometry creation is the rst step in CFD modelling, which is

done using a pre-processor. In this work, the 90 degree bend

(Fig. 1), has been created using the ANSYS Design Modeler.

Geometry with a total horizontal length of 150 in together with a

vertical length of 50 in has been designed in order to ensure fully

developed ow. Grid generation is a key issue in ow simulation

as it governsthe stability andaccuracy of theow predictions [38].

Forthe present case ofow througha 90 degree bend, unstructured

tetrahedral hybrid cells were used to discretize the entire ow

domain (Fig. 2). Grid independence study was carried out using

progressively larger number of cell elements. The results of the

grid independence study is shown in Figure 3. It can be seen that

there is practically no change in thepressure drop as thenumber of

grid is increased.

Governing Equations

The mass and momentum conservation equations are expressed as

follows:

Mass conservation:

@r

@t r r~u 0 1

Momentum conservation:

@

@t r~u r ruu~ rp r t 2

Wherer is the density, u is the velocity, p is the pressure, t is theviscous stress tensor.

Advanced turbulence models such as Direct Numerical

Simulation (DNS) can be useful to understand the physics of

turbulence, but requires powerful computing facility [39]. In this

work, oneof theRANS turbulencemodels, that is,the realizablek-

eturbulence model was found to be adequate to model turbulence.

The k and e equations are as follows:

@

@trk @

@xirkui @

@xjm mt

sk

@k

@xj

Gk re 3

@

@tre @

@xireui @

@xjm mt

se

@e

@xj

rC1Se C2r e

2

k ffiffiffiffiffinep4

Where Gkrepresents the generation of turbulence kinetic energydue to the meanvelocity gradients,S is themean strain rateand C1,

C2,skandse arethe model constants.The turbulent viscosity, mt is

computed as follows:

mt rCmk2

e 5

Where k, e are turbulent kinetic energy and turbulent kinetic

energy dissipation rate, respectively. Cm is computed from mean

strain and vorticity rate.

Figure 1 Geometry of the 90 degree bend.

Figure 2 Meshed geometry of the 90 degree bend.

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Boundary Conditions

Water at ambient temperature (300K) was used as the working

uid. Simulations were carried out by specifying velocity at the

inlet of the horizontal pipeline. Turbulent intensity, I and the

hydraulic diameter, Dh were specied for an initial guess of

turbulent quantities (k and e). The turbulent intensity was

estimated for each case based on the formula I 0.16(Re)1/8and was about 3% for all the cases. Outow boundary condition

was used at the outlet boundary.

Numerical Solution Strategy

The second-order upwind scheme was used for discretization of

the convection, turbulent kinetic energy and turbulent kinetic

energydissipationrate terms.SIMPLE algorithm wasemployed to

resolve the coupling between velocity and pressure elds.

The convergence criterion is based on the residual value of

calculated variables such as mass, velocity components, turbulent

kinetic energy (k), turbulent kinetic energy dissipation rate (e). In

the present calculations, the residual values were set at 104

for allvariables. The under-relaxation factors used for the stability of the

converged solutions were setat their default values.The numerical

simulation was decided as converged when the normalized

residual for each variable was less than the set residual value.

RESULTS AND DISCUSSION

In the ow of an incompressible uid through a horizontal section

of uniform pipe with no work input/output, the mechanical energy

balance can be written as [40].

P1 P2rg

XF

g 6

Where P is the static pressure ofow and r is the uid density,

while the subscripts indicate points 1 and 2, respectively. The term

F accounts for the friction losses, which include losses in the

straight pipe section (i.e. skin friction) and from pipettings (i.e.

form friction) in the system. These can be formulated as

X F

X 2fV2LD

XKfV2

2 7

Where f is the Fanning friction factor, which accounts for the skin

friction loss, V is the average velocity of the uid, L is the pipe

length and D is the pipe diameter. Kfis the dimensionless pressure

loss coefcient, which accounts for the form friction. The Fanning

friction factor is dened as [41]:

f DPs D2rV2L

8

WhereDPsis the pressure loss caused by the straight pipe section

of length L and Kfis dened as follows:

Kf2DPf

rV2 9

WhereDPfis the pressure loss caused by the pipe tting. A plot

between DPfand rV2/2 results in a straight line passing through

origin with Kf as the slope, which is the average value of the

pressure loss coefcient for the given ow condition. But, for

accurate determination of pressure loss, knowledge of loss

coefcient as a function of Reyolds number is essential. Figure 4

shows the comparison between loss coefcients from simulation

and published literature.

Hooper [42] developed an empirical two k method, which

correlates the loss coefcient with the Reynolds number and the

diameter of the tting through the following equation.

Kf K1Re

K1 1 1D

10

The K1and K1 values for the 90 degree bend are taken as

800 and 0.25 respectively and D is the diameter of the tting in

inches. It should be noted that this method is applicable only for

single-phase ow through pipettings. Several authors [15,22]

have modied this equation for the ow of complex uids and

ows and estimated the K1 and K1 values for both laminar and

turbulent regimes. Csizmadia and Hos [43] used experiments and

CFD modelling to determine the loss coefcient of Bingham and

Power law uids forow though diffuser and elbows. It can be

observed that the agreement between the K values is reasonably

good, particularly for Re

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better Kfvalues compared to the SST turbulence model used by[43]. From these results, students are able to appreciate the fact

that a validated CFD model is a very useful tool for the

determination of pressure loss coefcient of any combination of

tting and complex uid / ow.

The powerful post processing tools such as contour plots

enable students to visualize the contribution of form friction to the

pressure loss. The drastic change in ow velocity and the

separation of boundary layer around the bend (as highlighted) can

be easily observed from the contour plot (Fig. 5).

CONCLUSIONS

The usefulness of CFD simulation for the estimation of pressure

loss coefcients of pipe ttings has been demonstrated through asenior undergraduate project. The results are conclusive that a

validated CFD model is a cheap alternative for simulating

complex industrial ows and hence the determination of loss

coefcients. It is strongly believed that contour plots will help

students in the visualisation of uid ow phenomena such as

boundary layer separation.

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BIOGRAPHIES

Kumar Perumalobtained his PhD degree from

the University Institute of Chemical Technology

(UICT), Mumbai, India under the guidance ofPadmabhushan Prof. J.B. Joshi. Kumar is

currently an associate professor and associate

Deanfor Teaching and Learningin theFacultyof

Engineering and Science, Curtin University,

Sarawak Campus, Malaysia. His research inter-

ests include Computational Fluid Dynamics

(CFD), Fluids and Thermal Engineering, Pro-

cess Intensication Studies, and Engineering Education Research.

Rajamohan Ganesan is a senior lecturer of

Mechanical Engineering at Curtin University,

Sarawak, Malaysia and he obtained his PhD inMechanicalEngineering from Curtin University,

Perth, Australia. He received his MEng and

BEng degree fromthe BharathidasanUniversity,

India. His research interests are production of

power from low grade heat, mixed convection,

and radiation heat transfer.

CFD MODELING FOR THE ESTIMATION OF PRESSURE LOSS 185