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CFD Analysis of the Flow Through Tube Banks of HRSG
Conference Paper · January 2008
DOI: 10.1115/GT2008-51300
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1 Copyright © 2008 by ASME
Proceedings of ASME Turbo Expo 2008: Power for Land, Sea and Air
GT2008
June 9-13, 2008, Berlin, Germany
GT2008-51300
CFD ANALYSIS OF THE FLOW THROUGH TUBE BANKS OF HRSG
Marco Torresi
Dipartimento di Ingegneria Meccanica e
Gestionale
Politecnico di Bari
Via Re David, 200, Bari 70125, Italy
Tel: +39-080-596-3577, Fax: +39-080-596-3411
Email: m.torresi@poliba.it
Alessandro Saponaro
CCA Combustion & Environment Research Center
Ansaldo Caldaie
Gioia del Colle (BA), 70023, Italy
Tel: +39-080-348-0111, Fax: +39-080-348-1286
Email: Alessandro.Saponaro@ansaldoboiler.it
Sergio Mario Camporeale
Gestionale
Politecnico di Bari
Tel: +39-080-596-3627, Fax: +39-080-596-3411
Email: camporeale@poliba.it
Bernardo Fortunato
Gestionale
Politecnico di Bari
Tel: +39-080-596-3223, Fax: +39-080-596-3411
Email: fortunato@poliba.it
ABSTRACT
The prediction of the performance of HRSG (Heat
Recovery Steam Generator) by means of CFD codes is of great
interest, since HRSGs are crucial elements in gas turbine
combined cycle power plants, and in CHP (combined heat and
power) cycles. The determination of the thermo-fluid dynamic
pattern in HRSGs is fundamental in order to improve the
energy usage and limit the ineffectiveness due to non-
homogeneous flow patterns. In order to reduce the complexity
of the simulation of the fluid flow within the HRSG, it is useful
modeling heat exchangers as porous media zones with
properties estimated using pressure drop correlations for tube
banks. Usually, air-side thermo-fluid dynamic characteristics of
finned tube heat exchangers are determined from experimental
data. The aim of this work is to develop a new procedure,
capable to define the main porous-medium non-dimensional
parameters (e.g., viscous and inertial loss coefficients;
porosity; volumetric heat generation rate; etc…) starting from
data obtained by means of accurate three-dimensional
simulations of the flow through tube banks. Both finned and
bare tube banks will be considered and results presented. The
analysis is based on a commercial CFD code, Fluent v.6.2.16.
In order to validate the proposed procedure, the simulation of
an entire fired HRSG of the horizontal type developed by
Ansaldo Caldaie for the ERG plant at Priolo (Italy) has been
performed and results have been compared with their data.
KEYWORDS
CFD, HRSG, staggered tube bundle, porous media model,
pressure loss coefficients
NOMENCLATURE
C [m-1
] = inertial loss coefficient matrix
D [m-2
] = viscous loss coefficient matrix
d [m] = tube outer diameter
N = number of tube rows
P [Pa] = pressure
pl [m] = longitudinal pitch
pt [m] = transverse pitch
µ
ρ d
v
Re ∞
= = inlet Reynolds number
S [N/m3
] = source term vector of pressure loss

Uj [m/s] = j-component of the mean velocity
v [m/s] = velocity
∞
v [m/s] = inlet velocity
∞
= v
v
v*
= non dimensional velocity
α [deg] = inlet yaw angle
α’ [deg] = outlet yaw angle
γ [deg] = inlet pitch angle
i
n
∆ [m] = thickness of the medium in the ith
direction
i
P
∆ [Pa] = pressure drop in the ith
direction
2
*
2
1 ∞
∆
=
∆
v
P
P
ρ
= non dimensional pressure drop
γ’ [deg] = outlet pitch angle
µ [kg/ms] = dynamic viscosity
ρ [kg/m3
] = density
i j
u u
ρ [N/m2
] = i,j comp. of the Reynolds stress tensor
INTRODUCTION
Currently, combined cycle power plants result to be the
main alternative for standard coal- and oil-fired power plants
thanks to their high thermal efficiency, environmentally friendly
operation, and short time to construct. In the combined cycle
power plants, gas turbine and steam turbine cycles are
combined in order to optimize the exploitation of the energy of
a single fuel [1]. The high level of thermal energy contained in
the Turbine Exhaust Gases (TEG) is used in the HRSG in order
to obtain steam to be expanded in steam turbines. Actually, the
HRSG forms the backbone of combined cycle plants, providing
the link between the gas turbine and the steam turbine [2].
Fundamental parameters for HRSG are: pressure losses and
heat exchanged in the tube banks. Regarding the first point,
many theoretical and experimental works have been committed
in order to study different aspects starting from flow around
single cylinders, cylinders in tandem and sparse arrays of
cylinder. Nonetheless detailed information about densely
packed tube bundles is limited due to the complexity of the flow
[3].In order to improve the HRSG efficiency is crucial to have
uniform flow conditions through tube banks. However, due to
the HRSG complex geometry, especially in the first banks the
flow characteristics are far from being uniform. So, recently, an
effort has been made to use computational fluid dynamics
(CFD) analysis in order to investigate the gas-side flow path of
the HRSG. In such kind of simulations, tube banks are
frequently substituted by porous media zones that are equivalent
in terms of pressure drops and heat exchange to the original
tube banks [4], [5], [6]. The loss coefficients needed to
characterized the porous media model are often based on
pressure drop field measurements.
In order to have a predictive instrument to carry out
numerical simulations, in the present work a new approach is
proposed. Starting from accurate numerical simulations of a set
of tube bank configurations, simple correlations are determined
in order to be able to identify the actual loss coefficients to be
assign to each equivalent porous media zone.
CFD MODEL OF THE HRSG
In order to predict the performance of a fired HRSG, a 3D
thermo-fluid dynamic analysis has been carried out by means of
a commercial CFD code. The computational domain has been
generated by means of a 3D hybrid multi-block grid. The steady
incompressible three-dimensional RANS equations (eq. 1),
( )
0
j
j
j
i
i j i j
j j j j i
U
x
U
U
P
U U u u
x x x x x
ρ µ ρ
∂
=
∂
 
 
∂
∂
∂ ∂ ∂
=− + + −
 
 
 
∂ ∂ ∂ ∂ ∂
 
 
 
(1)
are discretised by means of a finite volume approach.
The pressure velocity coupling is achieved by means of the
SIMPLE algorithm (Semi-Implicit Method for Pressure-Linked
Equations). The convection terms and the pressure and viscous
terms are all discretised by means of a second order accurate
scheme. The Boussinesq approach is applied to relate the
Reynolds stresses to the mean velocity gradient. Turbulence has
been modeled by means of the standard k-ε model [7]. In order
to simulate the combustion of the post firing burners both the
Arrhenius reaction rates and the eddy-dissipation reaction rates
are taken into account by means of the finite-rate/eddy-
dissipation model. The radiative heat transfer is calculated by
means of the Discrete Ordinates (DO) model. In order to
consider the dependency of the absorption coefficient with
respect to the composition, the Weighted Sum of Gray Gases
Model (WSGGM) is used. The characteristic cell size method
has been applied to calculate the path length.
In order to carry out the CFD simulation of the entire
HRSG each heat exchange tube bank has been substituted with
an equivalent porous medium cell zones, in terms of pressure
losses and heat flux.
The porous media model
Porous media model can be used for a wide variety of
problems, including flows through packed beds, filters,
perforated plates, and tube banks [8].
When using this model, in the cell zones corresponding to
porous media, pressure losses are evaluated by means of
empirically determined flow resistance terms, composed of two
parts: a viscous loss term (Darcy’s Law) and an inertial loss
term. The porous media is modeled by means of an added

momentum sink in the governing momentum equations. The
source term is
1
2
S Dv v C v
µ ρ
 
=− +
 
 
. (2)
This momentum sink contributes to the pressure gradient in
the porous cell, creating a pressure drop that is proportional to
the fluid velocity (or velocity squared) in the cell. Since tube
banks are considered, the permeability or Darcy's term can be
neglected and only the inertial loss term taken into account. In a
Cartesian reference frame, this yields to the following
simplified form of the porous media equation:
{ }
1
, ,
2
i i i i
P C v n v i x y z
ρ
∆ = ∆ ∀ ∈ , (3)
where, ∆nx, ∆ny, and ∆nz are the thicknesses of the medium
respectively in the x, y, and z directions.
Heat transfer through the medium can also be represented,
subject to the assumption of thermal equilibrium between the
medium and the fluid flow, modifying the conduction heat flux
and the transient terms only. As a matter of fact, in the porous
medium, the conduction flux uses an effective conductivity and
the transient term includes the thermal inertia of the solid region
on the medium.
As far as concerns turbulence quantities, the code solves
standard conservation equations in the porous medium.
Moreover the effects of the porous medium on the turbulence
field is only approximated. As a matter of fact, the solid
medium has no effect on the turbulence generation or
dissipation rates. This assumption may be reasonable only if the
medium permeability is quite large, as in this case, and the
geometric scale of the medium does not interact with the scale
of the turbulent eddies. This is not strictly true in this case, but
there is no other possibility if the porous media model needs to
be used.
Fig. 1 Schematic of a tube bank
TUBE BANK SIMULATIONS
The main parameters of a tube bank are: the tube diameter,
d; the transverse pitch, pt; the longitudinal pitch, pl; the number
of rows, N (Fig. 1). As a first step a single row tube bank has
been considered and numerically simulated.
No end wall effects have been taken into account. In the
basic configuration, a tube row with a transverse pitch length,
pt, equal to 2.37 d is considered. In order to carry out the
simulations a computational domain has been defined and
meshed. Initially a 2D configuration has been considered. A
single tube has been drawn. The computational domain has
been meshed by means of a fully structured multi-block grid.
The domain is extended 5 tube diameters both upstream and
downstream.
Fig. 2 Computational domain for the default configuration
The tube has been placed in an interior square with a side
length of 1.58 d (Fig. 2). All around the tube wall 240 nodes
have been equally spaced. From the tube wall to the square
sides 80 intervals have a first-last ratio equal to 0.1. Upstream,
50 intervals have a first-last ratio equal to 0.2. Whereas
downstream, 100 intervals have a first-last ratio equal to 0.5. In
the two equal stripes, being attached in order to satisfy the
defined transverse pitch, 12 intervals each have a first-last ratio
equal to 0.7. Later on, when transverse pitch lengths equal to
3.16 d and 3.94 d are considered, 15 and 20 intervals have been
used respectively with the same first cell height.
In order to consider an infinite tube row, translational
periodic boundary conditions have been assumed in sides AD
and BC. At inlet AB, a uniform velocity distribution is imposed,
whereas, at outlet CD, a zero gauge pressure distribution is
imposed.
A parametric analysis has been performed in order to
evaluate the influence of the inlet flow conditions (Reynolds
number, yaw and pitch angles) on the default single row tube
bank, in terms of pressure drop and outlet angles. Actually, the
yaw angles are defined in the plain normal to the tube axes,
whereas the pitch angles are defined in the plain parallel to the
tube axes (Fig. 1). Moreover, the outlet values are computed as
Area-Weighted Average on the outlet boundary, which means
that every cell value is weighted by the corresponding cell area
on the boundary. When the effect of the inlet pitch angle, γ, is
under investigation, a 3D domain has been considered. Since no
end-wall effects have been taken into account, the domain
extends in the tube axial direction only of 0.03 d and axial
periodicity on the upper and lower walls has been imposed.

Default configuration
The reference inlet flow parameters are Re = 1 106
, α = 20
deg, γ = 0 deg. In Fig. 3 the contours of the non dimensional
velocity, v*, are reported. It is evident the wake downstream
and the flow acceleration through the tube row. Fig. 4 shows the
streamlines, which evidence the reduction of the yaw angle
downstream the tube row.
Fig. 3 Velocity contours @ Re = 1 106
, α = 20 deg, γ = 0 deg
Fig. 4 Streamlines @ Re = 1 106
, α = 20 deg, γ = 0 deg
Hence the tube bank tends to reduce velocity components
which are parallel to its plane. The non dimensional pressure
drop, ∆P*
, has been also computed and results to be equal to
0.5312.
Influence of the inlet condition
After the default simulation has been carried out, the
interest was to investigate the dependency of the global
parameters (i.e. non dimensional pressure drop and outlet yaw
and pitch angles) with respect to Reynolds number (Tab. 1),
inlet yaw angle (Tab. 2), and inlet pitch angle (Tab. 3).
As expected, when the Reynolds number grows, which
means (in this case) that the inlet velocity grows, the flow
experiences a corresponding increase of the pressure drop even
if the non dimensional pressure drop slightly decreases.
Furthermore the outlet yaw angle also decreases, which means
that the tube bank tends to rectify more efficiently the flow.
When the inlet yaw angle influence is considered, it is
possible to see that the outlet yaw angle varies almost linearly.
The reduction of the pressure drop following the yaw angle
increase it may be explained considering that in the different
simulations the inlet velocity magnitude is kept constant: hence
when the yaw angle grows, the inlet velocity component normal
to the tube bank (i.e. the flow rate across the tube bank)
decreases.
When the inlet pitch angle influence is taken into account,
analogous consideration can be done. The only difference is
that, the outlet pitch angle is only slightly lower than the
corresponding inlet pitch angle. This is due to the fact that only
one tube row in the tube bank is considered.
Tab. 1 Re effects; outlet condition @ α = 20 deg, γ = 0 deg
Re ∆P* α’ [deg]
5 105
0.5312 16.28
1 106
0.5148 16.07
2 106
0.4863 16.03
Tab. 2 Yaw angle effect; outlet condition @ Re 1 106
, γ = 0 deg
α [deg] ∆P* α’ [deg]
0 0.5807 0.00
10 0.5642 8.01
20 0.5148 16.07
Tab. 3 Pitch angle effect; outlet condition @ Re = 1 106
, α = 0 deg
γ [deg] ∆P* γ’ [deg]
0 0.5807 0.00
10 0.5524 9.89
20 0.5073 19.78
30 0.4378 29.70
Influence of the tube bank geometry
The geometrical parameters taken into account are only the
following: the transverse pitch length, the longitudinal pitch
length (i.e. the distance between tube rows in the tube bank),
and the number of tube rows considered in the tube bank.
The effect of the transverse pitch has been carried out on a
single row tube bank. Instead, in order to take into account the
effect of the longitudinal pitch, it was necessary to consider two
rows (i.e. the minimum possible number of rows).
When more than one row was considered in the tube banks,
tubes have been displaced exactly at mid transverse pitch with
respect to their upstream row. For this analysis only 2D
simulations have been performed. For instance no pitch angle
effect could have been considered. In Tab. 4 the outlet flow
conditions (in terms of non dimensional pressure drop and yaw
angle) are reported with respect to change in the transverse
pitch length. When the transverse pitch length grows, the tube
bank is coarse; for instance the pressure drop decreases and the
outlet yaw angle tends to be less different from the inlet yaw
angle.

When the longitudinal pitch effect is taken into account, it
is necessary to consider at least two rows in the tube bank. The
transverse pitch is kept equal to 2.37 d. In Tab. 5 the outlet flow
conditions are reported with respect to change in the transverse
pitch length for an inlet yaw angle equal to 20 deg.
First of all, since two tube rows are actually considered, it
is clear that the non dimensional pressure drop could double.
Tab. 4 Transverse pitch effect; 1 row; outlet condition @ Re = 1 106
,
α = 20 deg
pt/d ∆P* α’ [deg]
2.37 0.5148 16.07
3.16 0.3021 18.23
3.94 0.2193 18.52
Tab. 5 Longitudinal pitch effect; 2 rows; outlet condition @ Re =
1 106
, α = 20 deg, pt = 2.37 d
pl/d ∆P* α’ [deg]
2.37 1.0718 16.04
3.16 1.0479 13.01
3.94 1.0584 13.44
, α = 20 deg, pl = 2.37 d
, α = 20 deg, pl = 3.94 d
The results in terms of outlet yaw angle need more
attention. When the longitudinal pitch is 2,37 d, the wakes
downstream the first tube row don’t hit the tube in the second
row (Fig. 5). For instance the flow deflection in terms of yaw
angle is almost equal to the value obtained when only one row
is considered. Instead, when the longitudinal pitch is 3.16 d, the
wakes downstream the first tube row impinge the tubes in the
second row (Fig. 5). Hence there is an improvement in terms of
pressure drop, which decreases, and a stronger flow deflection
is evident.
In the case of longitudinal pitch equal to 3.94 d, same
considerations can be made as before. However, since the
position of the tubes in the second row is not anymore exactly
on the first row wakes (Fig. 6), the pressure drop is slightly
higher than before and the flow is slightly less rectified.
When the number of rows is taken into account it is evident
that the pressure drop grows as soon the number of rows
increases (Tab. 6). The trend is almost linear but the coefficient
of proportionality is greater than 1.
Tab. 6 Number of rows effect; outlet condition @ Re = 1 106
, α = 20
deg, pt = 2.37 d, pl = 2.37 d
N ∆P* α’ [deg]
1 0.5148 16.07
2 1.0718 16.04
3 1.5963 13.65
4 2.2415 11.41
The outlet yaw angle becomes lower when the number of
tube rows grows (Fig. 7, Fig. 8). This means that by increasing
the number of rows, it is possible to destroy any velocity
component which is parallel to the tube rows. Naturally this is
counterbalanced by an increase of pressure drop. It must be
said, that only one inlet yaw angle has been considered, which
means that particularly favored configuration with tubes aligned
to the upstream wakes have been neglected.
, α = 20 deg, N = 3

, α = 20 deg, N = 4
Finned tubes
Up to this point, only bare tubes have been considered.
Since in HRSG, in order to increase the heat exchange, finned
tubes are widely used, it could be interesting to simulate tube
banks with finned tube. Actually, in this work, only one type of
finned tube has been taken into account. The fins are 0.026 d
thick, 0.132 d wide and 0.342 d long. The fins are not directly
attached on the tube outer wall but they emerge from a stripe
(0.211 d wide), which forms a right-handed helix around the
tube with a helix pitch equal to 0.188 d. Every revolution has 30
fins (Fig. 9).
Fig. 9 Finned tube geometry
In this case it was necessary to define a 3D computational
domain (Fig. 10). The basic concepts inspiring the definition of
the computational domain are similar to the previous one. In
this case, in order to facilitate the discretization of the region
around the finned tube, an unstructured mesh was used (Fig.
11).
No end tube effect has been considered, so an infinite
finned tube bank has been considered. Translational periodic
condition has been imposed on the side wall of the
computational domain. The transverse pitch was kept equal to
2.37 d. The domain is extended in the direction of the tube axis
just for one helix pitch: on the upper and lower wall was again
imposed a translational periodic condition.
In order to limit the total number of cells, the domain is
only 4.74 d. The final mesh is made of 57668 cells.
Fig. 10 Computational domain for the finned tube banks
Fig. 11 Computational grid for the finned tube banks
The first set of simulations was carried out in order to
evaluate the flow behavior when the Reynolds number is
changed. Actually, the Reynolds number definition was kept
unchanged and still based on the outer bare tube diameter.
Looking at the simulation results (Tab. 7), one notices that,
despite the inlet pitch angle has been set to 20 deg, the outlet
pitch angles are very small, about 3.5-4 deg. This means that the
finned tubes are capable to reduce efficiently every large scale
flow structure, in particular when the Reynolds number is lower.
On the other end, the pressure drop results to be higher than
with bare tubes.
Tab. 7 Re effects; outlet condition @ α = 20 deg, γ = 20 deg
Re ∆P* α’ [deg] γ’ [deg]
1 106
1.0417 11.17 4.05
1 105
1.1149 5.67 3.90
2 104
1.5204 -3.28 3.63
Analogous consideration could be done in terms of yaw
angle. A particular note is required for the case at Re = 2 104
. In
this case, the outlet yaw angle becomes negative. This strange
behavior could be explained by considering that the fins on the
tube are displaced along a right-handed helix: when the flow

goes through the fins at low Reynolds number not only looses
the initial yaw angle but is also deflected in the opposite
direction (Fig. 12). On the other hand, when a left-handed helix
is considered at low Reynolds numbers, the deflection due to
the inclination of the fins counter-acts the tendency of the tube
banks to reduce velocity components which are parallel to their
plane.
Fig. 12 Different flow deflection when the Re changes
The next step is to consider the effect of the variation of the
inlet angles (both yaw and pitch angles) on the flow behavior.
Since these simulations are very time consuming, the number of
simulations has been limited changing simultaneously both the
yaw and the pitch angles (Tab. 8).
Tab. 8 Inlet angle effects; outlet condition @ Re = 1 106
α - γ [deg] ∆P* α’ [deg] γ’ [deg]
α = 0°; γ = 0° 1.3737 -6.50 0.30
α = 10°; γ = 10° 1.2682 3.33 2.06
α = 20°; γ = 20° 1.0417 11.17 4.05
The reduction of the pressure drop when the angles
increase could be explained considering that in all cases the
inlet velocity magnitude is kept unchanged, so that every time
the flow rate through the tube banks is actually decreasing. It is
also interesting to notice that when the yaw and the pitch angles
are both equal to zero, the fin geometry determine a deflection
of the flow (α’ = -6.50°; γ’ = 0.30°).
Finally, only the transverse pitch influence has been
considered, since the computational domain has been limited to
a single finned tube row.
Tab. 9 Transverse pitch effects; outlet condition @ Re = 1 106
,
α = 20 deg, γ = 20 deg
pt/d ∆P* α’ [deg] γ’ [deg]
2.37 1.0417 11.17 4.05
3.16 0.5596 13.53 8.99
3.94 0.4062 14.80 11.47
Tab. 10 Transverse pitch effects; outlet condition @ Re = 2 104
,
α = 20 deg, γ = 20 deg
pt/d ∆P* α’ [deg] γ’ [deg]
2.37 1.5204 -3.28 3.63
3.16 0.7410 4.41 8.50
3.94 0.5277 8.64 11.11
Both from Tab. 9 and Tab. 10, the following conclusions
can be made: when the transverse pitch length increases, the
pressure drop decreases as well as the deflection of the flow
both in terms of yaw and pitch angle.
POROUS MEDIUM CHARACTERIZATION
After having considered the previous large (but far to be
exhaustive) set of tube bank configurations, the main part of the
present work is to define correlation laws, which could allow
one to define porous media characteristics from tube bank
geometrical data and accurate numerical results even in
unexplored configurations.
The applied procedure is the following: the starting point is
the tube bank computational domain; the zone containing the
tube is deleted and substituted with a fluid zone without any
geometrical element; in the region equivalent to the tube bank is
then set the porous media model (Fig. 13).
Taking into account that the flow across tube banks is
highly turbulent, in the definition of the source term of pressure
loss inside the porous medium zone, the Darcy's term is
neglected and only the inertial loss term considered.
In order to validate the porous media model, the following
default configuration has been chosen: a single row of bare tube
has been considered with transverse pitch equal to 2.37 d; the
inlet flow is characterized by a Reynolds number equal to 1 106
and an inlet yaw angle equal to 20 deg and an inlet pitch angle
equal to 0 deg (for instance the preliminary geometry is 2D). In
this configuration, the inertial loss coefficients are empirically
defined in order to obtain the same outlet flow conditions. The
two characteristic inertial coefficients result to be: Cx = 9.250
[m-1
]; Cy = 7.40 [m-1
].

Fig. 13 Computational domain for the porous medium model
Once the coefficients have been defined at a specific flow
condition, the next step was to verify that the equivalent porous
medium is still capable to give reasonable response when the
inlet flow conditions are changed (Tab. 11).
From data reported in Tab. 11, the model results robust,
giving a maximum error of about 5%, which is considered
acceptable for the present analysis.
Tab. 11 Response of the porous medium model at inlet flow
conditions
Porous
medium
Reference
value
Error %
Inlet ∆P* α’ [°] ∆P* α’ [°] ∆P* α’
Re = 1 106
α = 20°
0.515 16.08 0.515 16.07 -0.08 -0.06
Re = 1 106
α = 10°
0.545 8.01 0.564 8.01 3.55 -0.04
Re = 1 106
α = 0°
0.555 0.00 0.581 0.00 4.63 -
Re = 2 106
α = 20°
0.515 16.08 0.486 16.03 -5.54 -0.31
Re = 5 105
α = 20°
0.515 16.08 0.531 16.28 3.10 1.24
Finally simple correlations have been determined in order
to get an estimate of the inertial loss coefficients with respect to
the main geometrical parameter of the tube bank.
The first geometrical parameter under investigation is the
transverse pitch length. A default 3D single row tube bank
configuration has been chosen as follow: Reynolds number
equal to 1 106
, yaw angle equal to 20 deg, pitch angle equal to
20 deg, transverse pitch length equal to 2.37 d. For the default
configuration the following optimal inertial loss coefficients
have been determined: Cx = 8.58 [m-1
], Cy = 2.90 [m-1
], Cz =
0.34 [m-1
] (Tab. 12). Then, other two transverse pitch lengths
have been considered: 3.16 d and 3.94 d. For each one, optimal
inertial loss coefficients have been determined too (Tab. 13 and
Tab. 14 respectively).
Tab. 12 Porous medium inertial loss coefficients for pt = 2.37 d
pt = 2.37 d, Re = 1 106
, α = 20°, γ = 20°
Inertial loss
coefficients
[m-1
]
C’x = 8.58 C’y = 2.90 C’z = 0.34
Tube bank
simulation
Porous medium
model
Error %
∆P* 0.4517 0.4520 0.0664
α’ [deg] 18.25 18.26 0.0548
γ’ [deg] 19.98 19.98 0.0000
pt = 3.16 d, Re = 1 106
, α = 20°, γ = 20°
Inertial loss
coefficients
[m-1
]
Cx = 5.12 Cy = 3.03 Cz = 0.25
Tube bank
simulation
Porous medium
model
Error %
∆P* 0.2696 0.2697 0.0371
α’ [deg] 18.18 18.18 0.0000
γ’ [deg] 20.04 20.05 0.0499
pt = 3.94 d, Re = 1 106
, α = 20°, γ = 20°
Inertial loss
coefficients
[m-1
]
Cx = 3.71 Cy = 2.50 Cz = 0.20
Tube bank
simulation
Porous medium
model
Error %
∆P* 0.1956 0.1956 0.0000
α’ [deg] 18.48 18.50 0.1082
γ’ [deg] 20.04 20.05 0.0499
From the previous data the following parabolic correlation
equations can be defined:
2
= 0.1914 - 1.5690 + 3.6434
'
x t t
x
C p p
C d d
   
   
   
(4)
2
= -0.1823 + 1.0650 - 0.5000
'
y t t
y
C p p
C d d
   
   
   
(5)
2
= 0.0943 - 0.8563 + 2.5000
'
t t
z
z
p p
C
C d d
   
   
   
(6)
The same approach has been used in order to define
parabolic correlations in order to take into account the
dependency with respect to the longitudinal pitch length (in a
two-row tube bank) (Tab. 15 - Tab. 17) and with respect to the
number of rows (Tab. 18 and Tab. 19). This time only 2D
simulations have been performed.

Tab. 15 Porous medium inertial loss coefficients for pl = 2.37 d
Pl = 2.37 d, pt = 2.37 d, Re = 1 106
, α = 20°, γ = 0°
Inertial loss
coefficients
[m-1
]
C’x = 7.70 C’y = 3.00
Tube bank
simulation
Porous medium
model
Error %
∆P* 1.0718 1.0722 0.1833
α’ [deg] 16.04 16.03 -0.0744
Pl = 3.16 d, pt = 2.37 d, Re = 1 106
, α = 20°, γ = 0°
Inertial loss
coefficients
[m-1
]
C’x = 6.3 C’y = 4.85
Tube bank
simulation
Porous medium
model
Error %
∆P* 1.0480 1.0437 -0.4103
α’ [deg] 13.01 13.01 0.0000
Pl = 3.16 d, pt = 2.37 d, Re = 1 106
, α = 20°, γ = 0°
Inertial loss
coefficients
[m-1
]
C’x = 5.48 C’y = 3.85
Tube bank
simulation
Porous medium
model
Error %
∆P* 1.05846 1.0604 0.1833
α’ [deg] 13.44 13.43 -0.0744
Tab. 18 Porous medium inertial loss coefficients for 3 rows
N = 3, Pl = 2.37 d, pt = 2.37 d, Re = 1 106
, α = 20°, γ = 0°
Inertial loss
coefficients
[m-1
]
C’x = 7.21 C’y = 3.2
Tube bank
simulation
Porous medium
model
Error %
∆P* 1.5963 1.5958 -0.0313
α’ [deg] 13.65 13.69 0.2930
Tab. 19 Porous medium inertial loss coefficients for 4 rows
N = 4, Pl = 2.37 d, pt = 2.37 d, Re = 1 106
, α = 20°, γ = 0°
Inertial loss
coefficients
[m-1
]
C’x = 7.4 C’y = 3.5
Tube bank
simulation
Porous
medium model
Error %
∆P* 2.2415 2.2373 -0.1874
α’ [deg] 11.41 11.31 -0.8764
Finally results of the dependency of the inertial loss
coefficients with respect to the transverse pitch length for finned
tube are presented (Tab. 20-Tab. 22).
When finned tubes are consider, difficulties are
experienced predicting the outlet yaw angle deflections. This is
mainly due to the difficulty of implement the effect of the
orientation of the finned helix.
pt = 2.37 d, Re = 2 104
, α = 20°, γ = 20°, finned tube
Inertial loss
coefficients
[m-1
]
C’x = 32 C’y = 200 C’z = 60
Tube bank
simulation
Porous
medium
model
Error %
∆P* 1.5204 1.5316 0.7366
α’ [deg] -3.27 0.06 wrong
γ’ [deg] 3.62 3.62 0.0000
pt = 3.16 d, Re = 2 104
, α = 20°, γ = 20°, finned tube
Inertial loss
coefficients
[m-1
]
Cx = 15.0 Cy = 53.0 Cz = 30.0
Tube bank
simulation
Porous
medium
model
Error %
∆P* 3.286 3.261 -0.7608
α’ [deg] 4.41 4.04 -8.3900
γ’ [deg] 8.50 8.62 1.4118
pt = 3.94 d, Re = 2 104
, α = 20°, γ = 20°, finned tube
Inertial loss
coefficients
[m-1
]
Cx = 7.9 Cy = 10.0 Cz = 19.0
Tube bank
simulation
Porous
medium
model
Error %
∆P* 2.3404 2.3245 -0.6794
α’ [deg] 8.64 8.76 1.3889
γ’ [deg] 11.11 11.13 0.1800
HRSG SIMULATION
In the last part of this work, a complete HRSG is simulated.
All the tube banks have been substituted with equivalent porous
media. The inertial loss coefficients, for each porous medium
cell zone, have been assigned taking into account the
description of the different tube banks (Tab. 23). In particular

only the effect of the transverse and longitudinal pitch lengths
and the number of rows have been taken into account, whereas
the geometry of the finned tubes have been neglected.
Tab. 23 Inertial loss coefficient for the HRSG simulation
Fig. 14 HRSG under investigation
The HRSG under investigation is a fired HRSG (with duct
burners) including a high and a low pressure section (Fig. 14)
developed by Ansaldo Caldaie for the ERG plant at Priolo
(Italy).
A completely structured multi-block mesh (481921 cells)
was applied in order to discretize the computational domain.
The main boundary conditions are reported in Tab. 24.
Tab. 24 Main boundary conditions
Thanks to the use of the porous media model, the
simulation of the HRSG at nominal load could have been
carried out satisfactorily. The flow coming from the turbine
diffuser enters the HRSG. As soon as the section of the HRSG
increases the flow separates giving origin to a very large
recirculation region (Fig. 15). For instance, the HP SH2 is not
crossed by an homogeneous flow, lowering its exchange
efficiency. The presence of the HP SH2 forces the flow to slow
down and have a more uniform distribution in the next heat
exchange section. Nevertheless a relatively high speed flow
interact with the upper level of the duct burners, which don’t
operate at their best conditions (Fig. 16). As soon as the first
heat exchange sections are crossed, the flow is equalized and
the contours of the gauge pressure become vertical (Fig. 17).
Fig. 15 Contours of velocity magnitude on a mid plane
Fig. 16 Contours of static temperature on a mid plane
Fig. 17 Contours of gauge pressure on a mid plane

In Fig. 18 the results in term of mean pressure distribution
are compared with results from an ANSALDO proprietary 1D
code.
The present simulation overestimates the pressure drop
across the HP SH2. The reason is that in the 3D numerical
simulation the second section of the high pressure super-heater
is crossed by a flow that is actually extremely not uniform,
whereas the 1D code takes into account a uniform flow
distribution. Nevertheless, it must be pointed out that globally,
the two codes give the same pressure drop.
Fig. 18 Mean pressure distribution
CONCLUSIONS
The aim of the present work was to determine the main
characteristics of the porous medium zones equivalent to real
tube banks, in order to carry out analysis on the thermo-fluid
dynamic behavior of HRSG. The HRSG, taken into account, has
been designed by ANSALDO CALDAIE for a Combined Cycle
with a topping Gas Turbine. The characterization of the porous
media has been performed on a numerical basis.
Many different tube bank configurations have been
simulated aiming to evidence the flow behavior dependency
with respect to both inlet flow and geometrical conditions.
Parameters, which have been taken into account, are: Reynolds
number, inlet yaw and pitch angles, transverse and longitudinal
pitch lengths, number of tube rows, finned or bare tubes.
For each configuration, an equivalent porous medium has
been assigned and numerically simulated optimizing the model
response in terms of outlet yaw and pitch angles and pressure
drop. Finally parabolic correlations have been extrapolated.
At the end, a complete HRSG has been simulated
characterizing each tube bank from default inertial loss
coefficients modified a priori by means of the defined parabolic
correlations. The results of the simulations have been compared
to equivalent analysis performed by ANSALDO CALDAIE, by
means of a proprietary 1D code. Results, in terms of the global
pressure drop across the entire HRSG, are in very good
agreement.
This is an initial work, which intended to test the proposed
methodology, which requires to increase the number of
parameters to be considered in order to obtain more general
results.
ACKNOWLEDGMENTS
We want to thanks Vincenzo Cavallo for his fundamentals
help in carrying out the numerical simulations.
REFERENCES
[1] V. Ganapathy, "Industrial Boilers and Heat Recovery
Steam Generators: Design, Applications, and
Calculations", Marcel Dekker Inc., New York, 2003.
[2] V.V. Sunil Kumar Vylta, G.P.G. Huang,"CFD Modeling
of Heat Recovery Steam Generators using Fluent",
30th Annual Dayton-Cincinnati Aerospace Science
Symposium.
[3] S.S. Paul, M.F. Tachie, S.J. Ormiston, "Experimental
study of turbulent cross-flow in a staggered tube
bundle using particle image velocimetry", Int. J. Heat
Fluid Flow 28, (2007) 441–453.
[4] P. Stehlik, "Heat transfer as an important subject in
waste-to-energy systems", Applied Thermal
Engineering 27 (2007) 1658–1670.
[5] S. Ahlinder, "On modelling of compact tube bundle
heat exchangers as porous media for recuperated gas
turbine engine applications", PhD thesis,
Brandenburgische Technische Universität Cottbus,
2006.
[6] Z.V. Stosic, V.D. Stevanovic, "A porous media
numerical prediction of void fraction and drift velocity
in two-phase flow across horizontal tube bundles",
Volume 2 - CHT'01 - Advances in Computational Heat
Transfer II, Proceedings of a Second Symposium -
Palm Cove, Queensland, Australia, May 20 - 25, 2001
[7] B.E. Launder, D.B. Spalding, “Lectures in
Mathematical Models of Turbulence”, Academic
Press, London, England, 1972.
[8] Fluent Manual, 2005. Fluent Incorporated. Centerra
Resource Park, 10 Cavendish Court, Lebanon, NH
03766.
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