Embed Size (px)
Citation preview
Journal of Structural Engineering Vol.61A (March 2015) JSCE
Aerothermal simulation and power potential of a solar updraft power plant
Hadyan Hafizh*, Hiromichi Shirato**
* Graduate Student, Dept. of Civil and Earth Resources Eng., Kyoto University, Katsura Campus C-1-3, Kyoto 615-8540
** Professor, Dept. of Civil and Earth Resources Eng., Kyoto University, Katsura Campus C-1-3, Kyoto 615-8540
In this paper we develop a theoretical model for calculating the steady inviscid flow
subjected to solar radiation at the collector of a solar updraft power plant. The result was a set
of nonlinear equation describing the transformation of the solar radiation into heat-flux of the
collector airflow. Iterative scheme was employed in order to solve the equation for mass flow
rate and temperatures, for which computer codes were developed. A comparison of
simulation results with the Manzanares prototype experimental data was performed;
demonstrating good agreement between the two. Computed power for selected locations in
Japan was also demonstrated for potential application of a solar updraft power plant.
Keywords: solar updraft power plant, aerothermal simulation, mathematical modeling
1. INTRODUCTION
An innovative design with old technology device to harness
the energy from solar radiation has been introduced through the
successful prototype project commissioned by the Minister of
Research and Technology of the Federal Republic of Germany at
Manzanares Spain. This device called the solar updraft power
plant (SUPP) or some researcher labeled it as the solar chimney.
The design and concept is attractive since it require renewable
source of energy therefore it is believed to be one of the clean and
safe future power plant.
The prototype has 194.6 meter (m) of tower height with
diameter of 10.16 m, and the collector has 244 m mean diameter
covered by different types of film-PVC with thickness of 0.1 mm.
The collector canopy was installed 2 m from the ground level. To
extract the kinetic energy from the updraft flow, 4-blade
vertical-axis wind turbine was placed at a height of 9 m from the
ground level and has 5 m of blade radius. With this configuration,
the prototype was able to produce 50 kilowatt of peak power1).
Basic idea of the SUPP is not entirely new since it is a
combination of three old technologies which are solar air
collector, chimney/tower, and wind turbine. The original idea in
order to harness the solar energy is by making use of the
greenhouse effect produced by the solar collector. Moreover, the
tower and the wind turbine were combined in an uncomplicated
system. The solar collector is composed by translucent covers
which allow the penetration of the electromagnetic wave from
the sun and simultaneously blocks the thermal radiation (infrared
wavelength). These mechanisms increase the internal energy of
the airflow and making the temperature larger than the ambient.
The hot air rises towards the tower due to buoyancy effects and
creates the updraft flow. A wind turbine is placed at the base of
the tower to convert kinetic energy from the updraft flow into
electrical energy. The whole process can be sustained as long as
there is a temperature differences between the airflow inside the
SUPP and the ambient air. The efficiency is low due to
conversion of thermal energy into pressure energy. In other
words, the high heat content (associated with high energy) within
the air is only used to create the necessary drive for the updraft
flow. According to Haaf2) the low efficiency is tolerated since it
involves extremely low costs and simplicity in the construction
and operation.
In the interest of increasing the system’s efficiency, it is
necessary to gain a comprehensive understanding of the airflow
aerothermodynamics. Thus the analysis presented herein focuses
on the mathematical model of collector airflow subjected to solar
radiation. Transformation of solar radiation into airflow heat-flux
will be modeled as well as extraction of kinetic energy from the
updraft flow. In addition, the effect of geometry to the
performance and mechanical power produced by SUPP are
discussed through numerical simulation. Finally, application of
SUPP is demonstrated for selected area in Japan.
2. MODELING
Mathematical model of SUPP shown in Fig. 1 as illustration
of the Manzanares prototype model is obtained by invoking the
principle of mass, momentum, and energy conservation. The
complete sets of governing equations are written in form of
differential equation as follows
Conservation of mass
Conservation of momentum
Conservation of energy
State equation
where represent the net body force per unit mass
exerted on the airflow e.g. gravity forces while
denotes the proper form of the viscous shear stress for each
component of spatial coordinate system .
Basically, there are four physical parameters needs to be
solved. They are density, velocity, pressure, and temperature. All
the physical parameter can be solved simultaneously with
addition of a state equation. Ideal gas model is selected as the
state equation which relates the temperature, density, and
pressure. The governing equation is often solved numerically
with help of the available computational fluid dynamics (CFD)
software. However, description of the nonlinear radiation
problem in most CFD solvers is difficult to trace, for example
transformation of solar radiation into thermal energy in form of
collector airflow heat-flux. Thus, we need a set of traceable
model which has capability to describe the transformation of
energy from solar radiation to thermal energy of collector airflow.
This model can be categorized from the simplest form which has
many assumptions and often far from the real condition to a
sophisticated model which employ fewer assumptions.
Despite of their limitation, these solvers are able to provide a
useful insight concerning the complex heat transfer phenomena at
the collector and often help engineers during conceptual and
preliminary design phase. Tractability of CFD radiation model,
motivate us to develop a solver which able to compute the
amount of heat-flux contained in airflow as a result of conversion
of solar radiation to thermal energy. Such solvers with their own
advantageous and limitation has also been developed by previous
researchers. Therefore it is necessary to summarize the previous
work as initial guidance in developing the mathematical model.
Nomenclature Greek Symbols
area [m2] absorptivity coefficient
specific heat capacity [J/kg K] thermal expansion coefficient [1/K]
specific internal energy [J/kg] gradient operator
the proper form of body force per unit mass [N/kg] difference operator
the proper form of the viscous shear stress [N/m3] emissivity coefficient
mass flow rate [kg/s] density [kg/m3]
pressure [N/m2] Stefan-Boltzmann constant [W/m2 K4]
r radial coordinate [m] transmissivity coefficient
rate of heat flux transferred to the airflow [W/m2]
the proper form of rate of volumetric heat addition Subscripts
per unit mass [W/kg] component of spatial coordinate system
the proper form of rate of heat due to viscous ambient air
effects [W/m3] airflow
ideal gas constant [J/kg K] cover
s spatial coordinate system [m] ambient ground
t time [s] ground
temperature [K] col collector
thrust force [N] rot rotor
velocity in scalar form [m/s] tow tower
velocity in vector form [m/s]
the proper form of rate of work done due to viscous Accents
effects [W/m3] vector
z axial coordinate [m] rate of change with respect to time
Fig.1 Illustration of a solar updraft power plant
2.1 Review of the mathematical model
Uncomplicated model based on the simplified governing
equations were proposed by Pastohr et al.3) which served the
purpose for comparison and parameter studies. They also make
use of CFD software (FLUENT) as basis of their numerical work.
The authors realized that the description of the operation mode
and efficiency has to be improved. Therefore they have carried
out an analysis to improve this issue. A pressure jump model was
selected in order to model the turbine. An iterative process was
followed thereafter. However, such scheme was reported to be
very time consuming. Therefore, they decided to use the Betz
power limit as pressure jump model at the turbine section.
Numerical simulation by Pastohr does not include radiation
model in their computation. Hence, the temperature of cover
surface and ground surface was assumed and treated as constant
value over the collector. In order to improve this numerical model,
Sangi et al.4) computes the temperature of cover, airflow, and
ground surface as function of collector radius. Thus, these
temperatures would serve as boundary condition in their CFD
simulation. Their numerical work was also based on CFD
software FLUENT. The authors not only conducted a numerical
simulation, but also utilized simple model as proposed by Pastohr.
Moreover, they also included the pressure model which was
solved via iterative scheme. Results from theoretical model with
inclusion of friction and numerical simulation were reported to be
consistent with the experimental data of the Manzanares
prototype.
A more sophisticated theoretical model was introduced by
Bernardes5) and Pretorius
6). Works by these two researchers were
mainly focused on the development of theoretical model and
numerical simulation of a solar updraft power plant. Significant
differences between the developed theoretical models are comes
from the applied heat transfer coefficients. Bernardes works
employ various heat transfer coefficients which most of them are
available in the heat transfer textbooks. As for Pretorius works,
the heat transfer coefficients were based on their recent
measurement. Moreover, these two authors collaborate in order
to compare their numerical simulation. Results of this
comparison have been reported in Bernardes et al.7)
and it was
found that both of theoretical model use different heat transfer
coefficients and had practically similar governing equations. In
terms of mechanical power and mass flow rate, these two
schemes agreed well. In conclusion, different theoretical model
and numerical scheme could produce similar results and hence
allowing a comparative study to be conducted.
A transient simulation under non-steady condition was
carried out by Hurtado et al.8) with CFD program
ANSYS-FLUENT as their basis computation. In order to take
into account of the ambient conditions, soil properties, cover
collector, and wind turbine behavior, the author has written series
of subroutines own programming language to be implemented in
the FLUENT’s User-Defined Function. This scheme is
interesting in particular since it altered the user-defined function
rather than let the CFD solver solve for all the physical
parameters. A recent publication made by Guo et al.9) also put
effort on the numerical simulation based on CFD program
FLUENT. Different with previous work with FLUENT, the solar
ray-tracing model provided by FLUENT has been implemented.
The ray-tracing model was used to calculate the effect of solar
radiation to the computational domain. This numerical work was
carried out for 3-D simulation since solar load available only for
3-D simulation. The author validated their numerical scheme
with the result of Manzanares data.
2.2 Mathematical Model of Solar Collector
Mathematical model for solar collector is evaluated from the
governing equations by choosing a suitable coordinate system
and employing several assumptions. The cylindrical coordinate
was chosen as the spatial coordinate system and the collector
airflow was modeled as inviscid and incompressible flow for
steady condition. Moreover, it was evaluated for one dimensional
case (axisymmetric flow). Transformation of solar radiation into
collector airflow heat-flux was modeled by evaluating the energy
balance at the cover surface, airflow, and the ground surface.
These assumptions have been made in order to simplify the
analysis of fluid part without simplifying the heat transfer part.
Applying the previous assumptions, the mass, momentum,
and energy conservation becomes
where and are radial air velocity and pressure at the
radial location in cylindrical coordinate system, an is
defined as the rate of heat flux transferred to the airflow.
Collector radius [rcol] = 122 m
Tower height [htow] = 194.6 m
Tower diameter [dtow] = 10.16 m
Solar tower
Solar collector
Wind turbine
Collector height [hcol] = 2 m
s3
z
r
s1
s2 θ
Eq. (1) – Eq. (3) have been simplified into Eq. (5) – Eq. (7)
for one dimensional, steady and inviscid flow which implies that
the gradient only in the radial direction, , and all
viscous terms are also becomes zero. We consider body forces
only applied in the tower airflow, thus . In addition,
we express in Eq. (3). Therefore, the
theoretical solutions of these equations can be derived as follows.
(1) Velocity Equation
We express the continuity equation i.e. Eq. (5) in terms of
mass flow rate as below
The collector system can be viewed as two parallel large
disks with fluid flowing in between. Moreover, the radial velocity
must be normal to the area of collector . Therefore the
radial fluid area can be written as and the
velocity profile in the radial direction is obtained as
Providing the value of and , the radial velocity for
a chosen geometry can be computed as shown in Fig. 2. From
Fig. 2 we can observe that the velocity is increasing from the
outer collector into the inner collector. It has dramatic increase of
velocity when they about to reach the center of collector.
(2) Pressure Equation
In order to obtain the profile of air pressure along the
collector, we have to convert the partial derivatives terms in Eq.
(6) into exact derivative form. Multiplying both sides of Eq. (6)
with and integrate them along the radius, yields
The above relationship is valid if the pressure and velocity are
function of collector radius only. The result of integration is
written in form of mass flow rate as
The static pressure was computed for selected value of mass
flow rate as shown in Fig. 3. From Fig. 3 we witness that the
static pressure is decreasing along the collector and drops when it
reached the center of the solar collector. Decreasing of static
pressure indicates that the dynamic pressure is increasing towards
the center of collector. It also implies that the velocity is
increasing toward the center and gives consistent result from
previous evaluation.
Fig.2 Radial air velocity for selected value of mass flow rate
Fig.3 Radial air pressure for selected value of mass flow rate
(3) Temperature Equation
It is useful to develop the concept of thermal resistance and
power balance for a solar collector to simplify the mathematics.
Consider the thermal network model for single cover of SUPP
system in Fig. 4.
Fig.4 Thermal network model for solar collector
0 20 40 60 80 100 120
100
101
Flow direction | Collector radius [m]
Velocity [m
/s]
dm/dt=1800 kg/s
dm/dt=1400 kg/s
dm/dt=1000 kg/s
dm/dt=600 kg/s
dm/dt=200 kg/s
0 20 40 60 80 100 120
-105
-100
-10-5
-10-10
-10-15
Flow direction | Collector radius [m]
-p
static [Pa]
dm/dt=1800 kg/s
dm/dt=1400 kg/s
dm/dt=1000 kg/s
dm/dt=600 kg/s
dm/dt=200 kg/s
Prior to Fig. 4, the heat balance equation can be established
for each evaluation points as follows
Cover surface
Collector airflow
Ground surface
The various heat transfer coefficients are defined as follows.
are the convection
heat transfer coefficients between cover and ambient air, between
cover and collector airflow, and between collector airflow and
ground respectively.
and
are the radiation heat transfer between cover
and sky, between ground and cover, and conduction heat transfer
between ground surface and ground at infinity respectively. is
denoted as Irradiance and are the
cover and ground absorptivity and cover transmissivity
respectively.
The objective was to solve the heat balance equation for
temperatures along the collector. In this equation we define three
unknown parameters which are temperature of cover ,
temperature of air , and temperature of ground . The rest
parameters are known such as Irradiance and ambient
temperature; they can be retrieved from daily or monthly
meteorological data. The sky temperature can be obtained as
function of ambient temperature as shown by Swinbank10)
.
Information concerning the optical properties of cover and
ground surfaces are widely available and their values depend on
the type of materials. As for the amount of heat transferred to the
airflow , we can access it through evaluation of Eq. (7). We
define this equation as the heat transport equation. Multiply both
sides of Eq. (7) with and integrate along the collector. The
heat transport equation becomes
In consideration of axisymmetric flow, Eq. (15) has been
multiply by . The letter and denotes the collector
height position. Furthermore, at the edge of collector the airflow
temperature is equal to the ambient air temperature. Substitute
this boundary condition we obtain
Fig.5 Radial air temperature for selected value of rate of heat-flux
Eq. (16) is solution of heat transport equation for air
temperature along the collector and its graphical solution is
presented in Fig. 5. Computation of Fig. 5 was conducted for
Manzanares geometry with prescribed mass flow rate and rate of
heat-flux. From this simple model we are able to obtain an initial
prediction of the temperature profile along the collector.
In order to conduct a more refine prediction of the airflow
temperature, we should take into account the convection heat
transfer process inside the solar collector. Therefore, our next
evaluation is about the heat balance equation. By evaluating this
equation, the process of energy transformation from solar
radiation into heat gain by the fluid can be explained. However,
our heat balance equation consists of three couple equations
which must be solved simultaneously for three temperatures i.e.
cover, air, and ground. Nevertheless, we can simplify our model
in order to obtain an initial prediction by assuming the cover, and
ground temperature as constant value. Thus, we only need one
equation which is Eq. (13). The convection heat transfer
coefficients hold a constant value along the radius and
was selected to be 50 W/m K, together with the specific heat
constant 1007 J/kg K. With these assumptions, we solve
the equation for temperature profile in radial direction by
substituting as boundary condition. It gives
where
Eq. (17) is solution of heat balance equation coupled with
heat transport equation and its graphical presentation is shown in
Fig. 6. Temperature profile in Fig.6 was also computed for
Manzanares geometry.
0 20 40 60 80 100 120
25
30
35
40
45
50
55
60
65
Flow direction | Collector radius [m]
Tem
peratu
re [0
C]
dq/dt=200 W/m2
dq/dt=400 W/m2
dq/dt=600 W/m2
dq/dt=800 W/m2
dq/dt=1000 W/m2
Fig.6 Radial air temperature for selected value of and
Temperatures of ground in Fig. 6 are always bigger than
temperature of cover since the ground absorbs more heat
from solar radiation than the cover. Values of and can be
arbitrarily selected as long as . In this work they have
been selected with constant difference for the sake of simulation.
Note the similarity of Eq. (16) and Eq. (17). The amount of
heat-flux which comes from solar radiation in Eq. (16) now has
been transformed to the airflow temperature via convection
process from the cover and ground surfaces. Despite its
simplicity, this model is able to provide useful information that
gives us knowledge about temperature profile along the collector.
However, this model is considered as a rough approximation. In
order to obtain more detail solution, we should evaluate all the
heat balance equation together with the heat transport equation.
Write Eq. (12), Eq. (13), and Eq. (14) in form of matrix and
define as temperature matrix, as heat flux matrix, and
as heat transfer coefficients matrix, we obtain
We might want to solve this equation immediately if matrix
is invertible. Such that . However, this
scheme is not complete. If we evaluate the expression of each
heat transfer coefficients, we would found that most of them are
function of the unknown parameters i.e. temperature of the cover,
air, and ground. The heat transfer coefficient and heat flux
matrices contain the unknown parameters as well. Directly
solving the matrix equation using inversion scheme would not
gives us a correct result. Thus we should look into the iterative
scheme and it is described in the aerothermal simulation section
of this paper.
2.3 Mathematical Model of Wind Turbine
A single wind turbine as shown in Fig. 7 has been selected to
be placed at the center of collector although SUPP often has more
than one turbine. Fig. 7 shows a stream-tube model for energy
extraction and the general device that represents this task is called
an actuator disk.
Fig.7 Stream-tube model for energy extraction by wind turbine
Generalized actuator disk theory was implemented in order to
describe the extraction of kinetic energy from the updraft flow.
During extraction of kinetic energy by wind turbine, flow at the
upstream of wind turbine experienced a “suction” force. This
force is best described as thrust (not to be confused with the
temperature ). Thrust can be described in terms of dynamic
pressure, rotor swept area , and coefficient of thrust .
Moreover, it can also be expressed as force acting on wind
turbine blades due to the pressure difference. Therefore, at any
plane of area within the control volume where there is
pressure difference associated with energy extraction, the Thrust
is written as
where and inflow coefficient with and without energy
extraction are given by Jamieson11)
as below
The air velocity at the rotor disc is expressed as
Therefore, we can write the above equations to obtain the
pressure drop across the rotor blades in terms of , such that
Fig. 8 presents the result of simulated pressure drop across the
rotor blade , where this physical quantity is shown in Fig.
7. Fig. 8 also demonstrates that low and small would not
give us an appreciable pressure drop.
0 20 40 60 80 100 120
25
30
35
40
45
50
55
60
65
Flow direction | Collector radius [m]
Tem
peratu
re [0C
]
Tc=400C & Tg=60
0C
Tc=450C & Tg=65
0C
Tc=500C & Tg=70
0C
Tc=550C & Tg=75
0C
Tc=600C & Tg=80
0C
Rotor region
Tower region
Collector region
Fig.8 Effects of mass flow rate and to the pressure drop
Effect of pressure drop across the rotor blade to the amount of
power extracted by wind turbine is described by the following
equation
Pressure drops implicitly affects the mechanical power
through the thrust force. Since the thrust force is depends on the
thrust coefficient (beside the dynamic pressure), thus we should
expect large thrust coefficient will result in large mechanical
power. Following our previous analysis, we should transform Eq.
(23) in terms of mass flow rate. We have a relation between
power coefficient and thrust coefficient. Upon substituting
this relation, it results in Eq. (24). Fig. 9 demonstrates the effect of
thrust and inflow coefficient to the mechanical power extracted
by wind turbine.
where is rotor blade radius and .
Fig.9 Effects of inflow coefficient and to the power
2.4 Mathematical Model of Solar Tower
Recall the governing equation for momentum i.e. Eq. (2) and
write the equation for axial direction ( as axial coordinate) with
inclusion of body force in form of gravity force and exclude
viscous force. The result is
where and z are airflow velocity through updraft
tower, density of airflow, pressure of airflow without energy
extraction ( in Fig. 7 is pressure of airflow with energy
extraction), acceleration of gravity, and axial direction of the
updraft tower.
In the present study, the approach for velocity analysis was
based on free convection process. Moreover, we employ the
Boussinesq model to our fluid in order to account for the effect of
variable density, only in the buoyancy forces. Substitute the
Boussinesq model into momentum equation we obtain
In order to integrate the equation along the solar tower height
( ), we should convert the partial derivative operator to the
exact derivative form. Multiply both sides of momentum
equation with results in
The left hand side of Eq. (27) represents the inertia force at
the collector region, and it is balanced with the buoyancy force at
the tower region. At this point, we can observe that the buoyancy
force provides the necessary condition to make the air start to
move or flowing. However, movement rate is usually low as it
witnessed from natural convection phenomena. The inertia force
is the one who responsible for making the air speed up or flowing
with significant rate. This inertia force is a result of the
aerodynamic entrainment. Combination of this entrainment effect
together with geometry of solar collector will produce a
significant airflow; start from the collector inlet to the collector
outlet (which is also regarded as tower inlet) and ended up at the
tower outlet.
Eq. (27) can be solved for velocity by substituting
. Thus, we should obtain identical expression of the
maximum velocity used by Schlaich et al.12)
in the analysis of
Manzanares solar updraft power plant. The result is in form
20
20
20
40
40
60
60
80
80
100
120
140
CT max
Pressure drop across the rotor blade
p [Pa]
Thrust Coefficient (CT)
Mass Flow
R
ate [kg/s]
0 0.2 0.4 0.6 0.8 1
0
200
400
600
800
1000
1200
1400
1600
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
0.01
0.02
0.0
3
0.0
4
0.0
5
CT max
dm/dt = 100 [kg/s]
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1
2
3
4
5
6
7
8
CT max
dm/dt = 500 [kg/s]
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
5
10
15
20
25
30
35
40
CT max
dm/dt = 900 [kg/s]
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
20
40
60
80
100
120
CT max
dm/dt = 1300 [kg/s]
Mechanical Power [kW]
In
flow
C
oefficien
ts (a)
Thrust Coefficients (CT)
3. AEROTHERMAL SIMULATION
In the previous analysis, most of the mathematical model was
function of mass flow rate and temperatures. In this section, we
will compute those parameters by taking into account the
complex heat transfer process at the collector. It leads to iterative
computation of the heat balance equation. By providing the
favorable initial guess, converging value of mass flow rate and
temperatures can be achieved. The complete procedure is
depicted in Fig. 10.
The computational and geometrical parameters as well as the
meteorological and optical data are served as input for simulation
process in Fig. 10. Values of these parameters are presented in
Table 1 and were used to simulate the aerothermal performance
of a solar updraft power plant. The outputs of simulation are the
temperatures and the mass flow rate.
Fig.10 Flow chart of developed computer code
Table 1 Parameters and boundary conditions used for
aerothermal simulation
Computational parameters Values Units
Maximum number of iteration
Maximum number of tolerance
Initial guess of mass flow rate kg/s
Initial guess of cover temperature K
Initial guess of air temperature K
Initial guess of ground temperature K
Geometrical parameters
Collector radius 122 m
Collector height 2 m
Tower radius 5.08 m
Tower height 194.6 m
Optical data
Cover absorptivity 0.04
Cover transmissivity 0.7
Cover emissivity 0.87
Ground absorptivity 0.9
Ground emissivity 0.9
Meteorological data
Irradiance As shown in Fig.11
Ambient air temperature As shown in Fig.11
To start a simulation, the information of computational and
geometrical parameters must be input to the program. After that,
the meteorological and optical data must be provided to allow the
program read these data. The thermal properties of airflow were
calculated according to the initially guessed values. Thermal
properties includes Nusselt number , Rayleigh number ,
Reynolds number , Prandtl number , and Hydraulic
diameter These thermal properties characterize the
convection process. The various heat transfer coefficient shown
in the Table 2 were then computed and the matrix equation i.e.
Eq. (18) were solved for temperatures. The mass flow rate was
also calculated according to Eq. (28). The current value of
temperature matrix and mass flow rate were then
compared with their previous value. Therefore, iterative process
was started to compute and until their value meet the
desired criteria. Converging value of and were then
used to estimate the mechanical power.
Fig.11 Radiation and ambient temperature data for simulation2)
0.00 6.00 12.00 18.00 24.00
0
20
40
60
80
100
0
200
400
600
800
1000
0.00 6.00 12.00 18.00 24.00
Am
bien
t T
em
peratu
re [
0C
]
Irrad
ian
ce [W
/m
2]
Time [hours]
Irradiance
Ambient Temperature
Yes
Yes
Yes
Yes No
No
No
No
Start
Start Initial Iteration
Time Step
Initial Iteration
Time Step Initial Guess of
Temperatures and
Mass Flow Rate
Initial Guess of
Temperatures and
Mass Flow Rate
Calculate
Thermal
Properties
Calculate
Thermal
Properties
Calculate Matrix
Equations
Calculate Matrix
Equations Solve for
Temperature and
Mass Flow Rate
Solve for
Temperature and
Mass Flow Rate Error
< Tolerance ?
Error
< Tolerance ?
Final Iteration
Time Step ?
Final
Iteration Time Step ?
Print Results
Print Results
End
End
Meteorological& Optical Data
Meteorological& Optical Data Geometrical Parameters
Geometrical Parameters Computational Parameters
Computational Parameters
3.1 Validation of Numerical Results
In order to confirm reliability of theoretical model and
validity of numerical simulation, comparison between numerical
results and experimental data of the Manzanares prototype has
been made. Fig. 12 shows the updraft velocity and mechanical
power vs Irradiance from simulation and experiment in which
good agreement has been obtained. Thus, the modeling and
simulation process can be used to predict the distribution of
velocity and temperature along the solar collector.
Fig.12 Comparison between experimental and numerical results
3.2 Velocity and Temperature Distribution
Fig. 13 presents the simulated temperatures and velocity
along the collector radius. The results were computed with
maximum Irradiance value in Fig. 11. In this case we have a
constant Irradiance value. For a constant solar radiation, the
simulated air temperatures increases toward the center of
collector. This pattern is also produced by the airflow velocity.
Since the maximum airflow velocity is at the center of collector,
it perfectly makes sense to install the turbine at this location.
Fig.13 Simulated temperatures, velocity, and mass flow rate
0 200 400 600 800 1000
0
3
6
9
12
15
0
3
6
9
12
15
0 200 400 600 800 1000
Up
darft V
elcoity [m
/s]
Irradiance [W/m2]
Experimental Data
Simulation Result
0 200 400 600 800 1000
0
10
20
30
40
50
0
10
20
30
40
50
0 200 400 600 800 1000
Mech
an
ical P
ow
er [kW
]
Irradiance [W/m2]
Experimental Data
Simulation Result
0 20 40 60 80 100 120
25
30
35
40
45
50
Length of Solar Collector [m]
Tem
peratu
re [0C
]
Cover Temperature
Fluid Temperature
Ground Temperature
0 20 40 60 80 100 120
0
5
10
15
Length of Solar Collector [m]
Rad
ial V
elocity [m
/s]
0 20 40 60 80 100 120
0
0.5
1
1.5
Mass Flow
R
ate [10
3kg/s]
Table 2 Heat transfer correlations and coefficients
Heat transfer
types Correlations Heat transfer coefficients References
Convection
(Free)
Bernardes et al. 5), 2003
Convection
(Free)
Bernardes et al. 7), 2009
Convection
(Forced)
Bernardes et al. 7), 2009
Radiation
Duffie and Beckman13), 2013
Radiation
Duffie and Beckman13), 2013
Conduction
Bergman, Lavine, Incropera, and
Dewitt,14) 2011
Table 2 Heat Transfer Correlations and Coefficients
Heat transfer
types Correlations Heat transfer coefficients References
Convection
(Free)
Bernardes et al. 5), 2003
Convection
(Free)
Bernardes et al. 7), 2009
Convection
(Forced)
Bernardes et al. 7), 2009
Radiation
Duffie and Beckman13), 2013
Radiation
Duffie and Beckman13), 2013
Conduction
Bergman, Lavine, Incropera, and
Dewitt,14) 2011
3.3 Performance Characteristics
Fig. 14 shows variation of mass flow rate and mechanical
power to temperature difference between collector airflow and
ambient air. They are computed for the Manzanares prototype
geometry. The mass flow rate was calculated according to Eq.
(28) for several inflow coefficient cases. Introducing the inflow
coefficient as an exploitation factor for the mass flow rate, Eq.
(28) becomes
in which , , , and are tower radius, tower
height, inflow coefficient, and thrust coefficient.
Converging value of from aerothermal simulation result
was used to estimate the amount of mechanical power as
depicted in Eq. (24). This was computed for selected value of
inflow coefficient. Upon examining graphical results in Fig. 14, it
is clear that the condition for inflow coefficient equals to zero was
the case for without turbine. According to Haaf2), the value of
inflow coefficient for the case with turbine is around 2/3, thus in
Fig. 14 they are written as a = 0.66. Mass flow rate and
mechanical power in Fig. 14 were computed with maximum
setting of thrust coefficient ( .
Fig.14 Simulated mass flow rate and mechanical power
3.4 Effects of Geometry
Effects of collector radius and tower height to the mechanical
power and airflow temperature have been analyzed and its
graphical results are presented in Fig. 15. Simulation was
conducted for Irradiance value equal to 1000 W/m2, with
maximum setting of thrust coefficient. The value of inflow
coefficient was set for 2/3 and mechanical power was computed
for collector radius and tower height up to 250 m. It was found
that the geometry plays important role in the production of power.
The longer the collector radius and the higher the tower height is,
the greater the power generation will be. Therefore, these results
suggested that there is no optimum configuration of a solar
updraft power plant. However, optimizing the design of a SUPP
could be done through optimum design of wind turbine.
Moreover, arrangement and installation of wind turbine is also
has significant effect to the power production. If we include cost
as optimization parameters, thus the optimum design and
configuration may also affected by the initial capital cost and
interest rate.
Increasing the size of a solar updraft power plant does not
necessarily followed by rapid increment of airflow temperature as
shown in Fig. 15. The airflow heat-flux is always balance with
the convection, conduction, and radiation process at the collector
as depicted in Eq. (12), Eq. (13), and Eq. (14). Nevertheless, it is
desirable to have a collector system with minimal heat-losses.
Fig.15 Effects of geometry to the power and airflow temperature
0 2 4 6 8 10 12 14 16 18 20 22 24
0
300
600
900
1200
1500
a=0.93
a=0.86
a=0.77
a=0.66
a=0.53
a=0.37
a=0.19
Mass Flow
R
ate [kg/s]
T [0C]
Without turbine case
With turbine case
0 2 4 6 8 10 12 14 16 18 20 22 24
0
50
100
150
200
a=0.93
a=0.86
a=0.77
a=0.66
a=0.53
a=0.37
a=0.19
Mech
an
ical Pow
er [kW
]
T [0C]
Without turbine case
With turbine case
4. POWER POTENTIAL IN JAPAN
The following chapter discusses the power potential of a solar
updraft power plant for selected locations in Japan. Four cities
were selected for theoretical calculation of monthly mean energy,
namely, Shizuoka, Miyazaki, Kochi, and Ishigakijima, where
solar radiation is stronger than other locations in Japan. These
four cities are located in different regions of Japan; Honshu island
for Shizuoka, Kyushu island for Miyazaki, Shikoku island for
Kochi, and Okinawa region for Ishigakijima. Locations of each
area are marked in the solar radiation map (Fig. 16) provided by
NEDO15)
(New Energy and Industrial Technology Development
Organization).
The monthly mean meteorological data, necessary for
calculation of theoretical energy output are provided by the Japan
meteorological agency (JMA) and atmospheric science data
center NASA. The solar radiation data, together with the monthly
mean temperature are accessed through the JMA and NASA
websites. These meteorological data serve as input for
computation of theoretical energy output. Procedure to calculate
the theoretical energy output is similar with those described in
aerothermal simulation section.
Fig.16 Selected locations for theoretical energy output calculation
Fig. 17 shows the calculated mean energy output for 4 cities
in Japan. Result of the Manzanares prototype, provided by
Schlaich et al.12)
was used for comparison. Since the original
meteorological data for Manzanares results was not available in
the literature, thus we use meteorological data from the
atmospheric science data center NASA17)
for simulation.
Simulation result produces 6% deviation from the experiment in
term of yearly mean energy production. Despite different pattern
of monthly mean energy, the 4 cities in Japan have relatively
small difference in term of yearly mean energy production.
Fig.17 Calculated daily, monthly, and yearly mean energy
0
50
100
150
200
250
300
Jan
Feb
Mar
Ap
r
May
Ju
n
Ju
l
Au
g
Sep
Oct
Nov
Dec
En
ergy [kW
h/d
ay]
Monthly mean energy production
Shizuoka
Kochi
Miyazaki
Ishigakijima
Manzanares (Simulation)
Manzanares (Experiment)
Table 3 Monthly mean meteorological data16)
Months Mean Global Solar Radiation [MJ/m
2] Mean Temperature [
0C]
Shizuoka Miyazaki Kochi Ishigakijima Manzanares17)
Shizuoka Miyazaki Kochi Ishigakijima Manzanares17)
January 10.9 11.5 10.9 10.1 7.7 5.7 6.8 5.8 18.7 3.6
February 11.9 12.1 12.3 13 11.0 7.3 9.4 7.8 21.2 5.3
March 15.9 15.2 15.3 14.8 15.4 13.3 13.8 12.7 22 9.4
April 18.6 19.3 19.7 12.4 18.9 15.4 15.6 14.8 22.3 12.0
May 20.5 20.6 20.4 17.9 21.8 19.2 20.3 19.9 26 17.1
June 15.3 12 13.8 22.1 25.5 22.6 23.2 23.2 29.2 23.0
July 17.6 21.7 20.4 24.3 26.5 26.4 29 28.1 29.5 26.4
August 19.2 20.8 19.6 20.4 22.7 28.4 29.3 29 29.7 25.6
September 17.2 16.5 15.4 19.8 17.1 25.4 24.9 24.9 28.5 20.8
October 10.9 12.3 11.9 14.4 11.6 21.1 20.6 20.7 25.7 14.8
November 10.7 11.6 10.5 10.9 8.2 13.1 13.5 12.9 22.6 8.6
December 9.7 10.1 9.8 6.3 6.6 8.2 8.1 7.4 18.7 4.9
Average 14.9 15.3 15.0 15.5 16.1 17.2 17.9 17.3 24.5 14.3
Table 3 Monthly mean meteorological data16)
Months Mean Global Solar Radiation [MJ/m
2] Mean Temperature [
0C]
Shizuoka Miyazaki Kochi Ishigakijima Manzanares17)
Shizuoka Miyazaki Kochi Ishigakijima Manzanares17)
January 10.9 11.5 10.9 10.1 7.7 5.7 6.8 5.8 18.7 3.6
February 11.9 12.1 12.3 13 11.0 7.3 9.4 7.8 21.2 5.3
March 15.9 15.2 15.3 14.8 15.4 13.3 13.8 12.7 22 9.4
April 18.6 19.3 19.7 12.4 18.9 15.4 15.6 14.8 22.3 12.0
May 20.5 20.6 20.4 17.9 21.8 19.2 20.3 19.9 26 17.1
June 15.3 12 13.8 22.1 25.5 22.6 23.2 23.2 29.2 23.0
July 17.6 21.7 20.4 24.3 26.5 26.4 29 28.1 29.5 26.4
August 19.2 20.8 19.6 20.4 22.7 28.4 29.3 29 29.7 25.6
September 17.2 16.5 15.4 19.8 17.1 25.4 24.9 24.9 28.5 20.8
October 10.9 12.3 11.9 14.4 11.6 21.1 20.6 20.7 25.7 14.8
November 10.7 11.6 10.5 10.9 8.2 13.1 13.5 12.9 22.6 8.6
December 9.7 10.1 9.8 6.3 6.6 8.2 8.1 7.4 18.7 4.9
Average 14.9 15.3 15.0 15.5 16.1 17.2 17.9 17.3 24.5 14.3
Selected Locations
Selected Locations
5. CONCLUSION
This paper begins with the overview of a solar updraft power
plant following by the current development of their mathematical
models. Upon reviewing the available models, a set of theoretical
model for solar collector part was proposed in order to explain the
complex transformation of solar radiation to the collector airflow
heat-flux. A simple yet powerful theory, namely, generalized
actuator disk theory, concerning kinetic energy extraction of a
wind turbine was implemented. It was found that the amount of
kinetic energy extraction can be modeled through the inflow
coefficient which its value should be obtained from experimental
data. Free convection analysis was performed for solar tower part
with purpose to obtain the model of mass flow rate. The model
itself is consistent with the model used by Schlaich et al.12)
in the
analysis of maximum velocity. All the developed models were
combined to form a procedure to calculate velocity, temperatures,
and mechanical power of a solar updraft power plant. The
procedure was elaborated and validated in the aerothermal
simulation section of this paper. Finally, potential application of
SUPP was successfully demonstrated through estimation of
theoretical mean energy output for selected locations in Japan.
ACKNOWLEDGEMENT:
The first author gratefully acknowledges the Ministry of
Education, Culture, Sports, Science and Technology (MEXT) of
Japan for the Japanese government (Monbusho) scholarship.
APPENDIX
The temperature matrix, heat-flux matrix, and heat transfer
coefficients matrix, of Eq. (18) are given as follows
where
References
1) Haaf, W., Friedrich, K., Mayr, G., Schlaich, J., Solar
Chimneys Part I: Principle & Construction of the Pilot Plant
in Manzanares, Int. J. Solar Energy, Vol. 2, pp. 3-20, 1983.
2) Haaf, W., Solar Chimneys Part II: Preliminary Test Results
from the Manzanares Pilot Plant, Int. J. Solar Energy, Vol. 2,
pp. 141-161, 1984.
3) Pastohr, H., Kornadt, O., Gurlebeck, K., Numerical and
analytical calculations of the temperature & flow field in the
upwind power plant, Int. J. Energy Res., 28, 495-510, 2004.
4) Sangi, R., Amidpour, M., Hosseinizadeh, B., Modeling and
numerical simulation of solar chimney power plants, Solar
Energy 85, 829-838, 2011.
5) Bernardes, M. A., Voß, A., Weinrebe, G. Thermal and
technical analyses of solar chimneys, Solar Energy, 75,
511-524, 2003.
6) Pretorius, J. P., Solar tower power plant performance
characteristic, MSc Thesis, Stellenbosch University, 2004.
7) Bernardes, M. A., von Backstrom, T. W., Kroger, D. G.,
Analysis of some available heat transfer coefficients
applicable to solar chimney power plant collectors, Solar
Energy 83, 264-275, 2009.
8) Hurtado, F. J., Kaiser, A. S., Zamora, B., Evaluation of the
influence of soil thermal inertia on the performance of a
solar chimney power plant, Energy, 47, 213-224, 2012.
9) Guo, P., Li, J., Wang, Y., Numerical simulations of solar
chimney power plant with radiation model, Renewable
Energy, 62, 24-30, 2014.
10) Swinbank, W. C., Long-wave radiation from clear skies, Q.
J. R. Meteoro. Soc. 89:339, 1963.
11) Jamieson, P., Generalized limits for energy extraction in a
linear constant velocity flow field, Wind Energy,
11:445-457, 2008.
12) Schlaich, J., Bergermann, R., Schiel, W., Weinrebe, G.,
Design of commercial solar updraft tower systems –
Utilization of solar induced convective flows for power
generation, J. Sol. Energy Eng,. Vol. 127, 117-124, 2005.
13) Duffie, J. A., Beckman, W. A., Solar Engineering of
Thermal Processes, John Wiley & Sons, Inc., 2013.
14) Bergman, T. L., Lavine, A. S., Incropera, F. P., Dewitt, D. P.,
Fundamentals of Heat and Mass Transfer 7th Edition, John
Wiley & Sons, Inc: New Jersey, 2011.
15) NEDO, Guidelines for PV Power Generation Field Test
Project (Design, Construction and System), 2010.
16) Tables of Monthly Climate Statistics, Retrieved from
http://www.data.jma.go.jp, [Accessed 1/10/2014].
17) NASA – SSE Release 6.0 Data Set, Retrieved from
http://eosweb.larc.nasa.gov, [Accessed 14/1/2015].
(Received September 24, 2014)
(Accepted February 1, 2015)
