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2011-12-16
Advanced Energy EstimationsProject Assignment HunflenPaul Hines & Haseeb Ahmad
12/15/2011
Examiner: Stefan Ivanell
This report will use the software WindSim to estimate the annual energy production of 3turbines at Hunflen in Sweden. Turbulence model RNG and Wake Model 1 will be employedin the simulation in WindSim.
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1. Introduction ..................................................................................................................................... 5
1.1. Background ............................................................................................................................. 5
1.2. Aim and question formulation ................................................................................................. 5
1.3. Delimitations ........................................................................................................................... 6
2. Theoretical framework .................................................................................................................... 6
2.1. Navier-Stokes equations .......................................................................................................... 6
2.2. Turbulent Flow Solutions ........................................................................................................ 6
2.2.1. Reynolds Averaged Navier-Stokes Equations ................................................................. 7
2.2.2. Direct Numerical Simulation (DNS) ............................................................................... 9
2.2.3. Large eddy simulation (LES) .......................................................................................... 92.2.4. Detached eddy simulation (DES) .................................................................................... 9
2.3. Weibull distribution ............................................................................................................... 10
3. Analysis ......................................................................................................................................... 10
3.1. Methodology ......................................................................................................................... 10
3.1.1. Wake effects .................................................................................................................. 13
3.1.2. Turbulence model .......................................................................................................... 14
4. Results ........................................................................................................................................... 15
4.1. Production according to vindstat.nu ...................................................................................... 15
4.2. WindSim Results ................................................................................................................... 16
4.2.1. Wake model 1 ................................................................................................................ 16
4.2.2. Wind Resources ............................................................................................................. 19
4.3. Comparison with other Turbulence models .......................................................................... 20
5. Discussion ..................................................................................................................................... 22
5.1. VilhelmVestas V52 ........................................................................................................... 22
5.2. FerdinandVestas V52 ........................................................................................................ 22
5.3. Freja NEG Micon 52 ............................................................................................................. 23
6. Conclusion ..................................................................................................................................... 23
Bibliography .......................................................................................................................................... 24
Appendices ............................................................................................................................................ 25
Table of Contents
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Figure 1 Turbulence flow solution techniques ........................................................................................ 7
Figure 2 Sample output of energy module ............................................................................................ 10
Figure 3 Cell resolution at 5000 ............................................................................................................ 11
Figure 4 Cell resolution at 300000 ........................................................................................................ 11
Figure 5 Power curve Vestas V52 850 .................................................................................................. 12
Figure 6 Power curve NEG Micon 52 900 ............................................................................................ 12
Figure 7 Objects as placed in terrain module ........................................................................................ 13
Figure 8 Yearly output 2009-2010 Ferdinand from vindstat.nu ............................................................ 15
Figure 9 Yearly output Vilhelm 2009-2010 from vindstat.nu ............................................................... 15
Figure 10 Power output from WindSim frequency table ...................................................................... 16
Figure 11 Power output per turbineFrequency .................................................................................. 16
Figure 12 Estimated productionactual production Frequency table .................................................. 17
Figure 13 Actual vs estimated production frequency table ................................................................... 17
Figure 14 Power output from WindSim frequency table ...................................................................... 17
Figure 15 Power output per turbineWeibull distribution................................................................... 18
Figure 16 Estimated productionactual production Weibull distribution ........................................... 18
Figure 17 Actual vs estimated production frequency table ................................................................... 19
Figure 18 Wind Resource map and Wind Rose at 300000 cell resolution ............................................ 19
Figure 19 Turbulence model comparisonFerdinand .......................................................................... 21Figure 20 Turbulence model comparison - Freja .................................................................................. 21
Figure 21 Turbulence model comparison - Vilhelm ............................................................................. 22
List of Figures
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1. Introduction1.1. BackgroundIn spite of early discussion questioning the profitability of wind power in forest
environments (Wizelius) interest in harvesting wind resource from complex/ and or hilly
terrain is growing in for example in Sweden with a number of projects in planning. Vindkraft
Norr is a joint venture between Statkraft, a large energy company and SCA a company
owning large amounts of forest land (vindkraftnorr.se) . The absence of a nearby residential
population can making planning easier but often the terrain can be more challenging.
The first software providing wind resource estimations was developed in the 1980s.
Windpro, a modular based Windows compatible software that can be used for design and
planning of individual wind turbines or wind farms was developed over 20 years ago in
lborg in Denmark. WAsP, the Wind Atlas Analysis and Application Program enables wind
simulation and estimation of power output from wind turbines through the use of linear
equations and has been in present in the industry for over 25 years (Facts about Ris DTU).
However, the limitations of this software in complex terrain have been recognized (Wallbank,
2008)
Software models such as Windpro using computational fluid dynamics (CFD) have beenseen to have considerable advantages when mapping complex terrain. The founder of
WindSim, Arne Grawdahl was working on the project to establish the Norwegian Wind Atlas.
The use of CFD was required to simulate the complex Norwegian coastline. The first
commercially available version of WindSim was launched in 2003.
CFD will be examined later in a discussion of the theoretical framework underlying this
study.
1.2. Aim and question formulationThis report will use the software WindSim to estimate the annual energy production of 3
turbines at Hunflen in Sweden. Hunflen lies in Dalarna in mid Sweden. The turbines are two
Vestas V52 and one NEG Micon 52.
Turbulence model RNG and Wake Model 1 will be employed in the simulation in WindSim.
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1.3. DelimitationsThis report is produced under limited time frame and by users who are not well skilled in
the use of CFD software. The users have the benefit of direction and assistance from members
of the department of wind power at Gotland University but even given WindSims user
friendly interface both of the above limitations much be acknowledged.
2. Theoretical frameworkCFD uses a non-linear flow model based on Navier-Stokes equations. Navier-Stokes
equations describe fluid flow based on the laws of conservation of momentum, mass and
energy. (Karl Nilsson, Stefan Ivanell, 2010)
2.1. Navier-Stokes equationsNavier-Stokes equations are used to explain the motion of a fluid i.e. liquid or gas. These
equations are based on Newtons Second Law which describes the relation between force,
mass and acceleration on a fluid. Navier Stock equations are quite useful in the modeling of
weather, understanding the flow behavior of fluids, designing of wind turbines blades,
aircraft, and in many other useful applications.
Navier-Stokes Equations are non-linear, partial differential equations which do notexplicitly describe the variables but these present how variables change with time. The
solution of Navier-Stokes Equations is velocity field which describe the velocity of fluid at a
point in time. (T. Wallbank, 2008). The assumption, on which Navier-Stokes equations are
based, is the continuous nature of fluid. The derivation of Navier-Stokes equations starts with
the conservation of mass, momentum and energy conservation for a finite arbitrary volume.
(T. Wallbank, 2008)
2.2. Turbulent Flow SolutionsThe turbulence can be defined as the state of motion of a fluid which is characterized by
apparently random and chaotic three dimensional vorticity. (Introduction to turbulence/Nature
of turbulence, 2011) Vorticity can be defined as the measure of the rate of rotational spin in a
fluid. Turbulence dominates all other flow phenomena, and results in increased energy
dissipation, mixing, heat transfer, and drag.
Turbulent flows can be computed either by solving the Reynolds Average Navier-Stokes
(RANS) equations with suitable models or with direct computation.
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2.2.1. Reynolds Averaged Navier-Stokes EquationsThe Reynolds Averaged Navier-Stokes Equations are the simplification of Navier-Stokes
Equations by taking the time average of the velocity terms in the equations. RNS equations
are used to describe turbulent flows. The basic tool which is required to derive the RNS
equations from Instantaneous Navier-Stokes equations is the Reynolds decomposition. The
Reynold decomposition means the separation of variable into the mean (time averaged)
component and fluctuating component. By this transformation, we get a set of unknowns
called Reynold Stresses which are the functions of velocity fluctuations and which require a
turbulence model to produce a closed system of solvable equations. The computational
requirements for RANS equations are far less than Navier-Stokes equations. (symscape, 2009)
Turbulence ModelsTurbulence modeling is used to calculate the effects of turbulence in fluids. By taking
average, the solution of turbulence equations can be simplified but models are required to
represent scales of the flow that are not resolved. (Ching Jen Chen, 1998)
Figure 1 Turbulence flow solution techniques
RANS based
turbulence
models
Large eddy
simulation (LES)
Detached eddy
simulation (DES)
Direct Numerical
Simulation DNS
Linear eddy
viscosity Models
Non-Linear eddy
viscosity Models
Reynolds stress
Models
Algebric Models One equation
Models
Two equation
Models
k-epsilon Model k-omega ModelRealisability
Issues
Near Wall
Treatment
RNG k-epsilon
Model
Realisable k-
epsilon Model
Standard k-
epsilon Model
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Following turbulence model is used in WindSim
K epsilon turbulence model
k-epsilon turbulence model is one of the most common turbulence models however it does not
work well in the cases where large pressure gradient occurs. (Wilcox, 1998, p. 174). Thismodel came from the main branch of turbulent solution techniques i.e. RANS based
turbulence models. The sub-branch of RANS based turbulence models is the linear eddy
viscosity models, it can be seen in figure below. It is a two equation turbulence model which
means it employs two extra transport equations to describe turbulent flow behavior.
The first transported variable is turbulent kinetic energy and second transported variable is
turbulent dissipation.
Turbulent kinetic energy
The turbulent kinetic energy is simply the energy in the turbulence. If the flow can be
partitioned into mean and turbulent parts, then the total kinetic energy of the flow will simply
be the sum of the kinetic energy of the mean and turbulent flows. (Turbulence Intensity and
Turbulent Kinetic Energy, 2011)
Turbulent dissipation
Turbulent dissipation describes the scale of the turbulence.
Some usual models of k-epsilon models are
Standard k-epsilon model
Realisable k-epsilon model
RNG k-espsilon model
WindSim uses k-epsilon as the turbulent model with standard form as well as modified
forms. The standard k-epsilon model is widely used turbulent model and has been verified
and validated for a wide variety of flows. It has less computational costs and is numerically
more stable than the more advanced and complex stress models, it is more successful in flow
where the normal Reynolds stresses are less important. In wind engineering, k-epsilon model
doesnt perform well because its inability to cope w ith normal stresses which are more
dominant in wind flows. (Veersteeg, H.K., and Malalasekera, W., 1995)
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WindSim uses some modified k-epsilon models like RNG k-epsilon model, k-epsilon
model with YAP correction. The RNG k-epsilon is based on the renormalization group
analysis of the Navier-Stoke equations. The transport equations for turbulence generation and
dissipation are the same as those for the standard model but the model differs because of one
additional constant which improves the performance for separating flow and recirculation
regions.
One of the main inadequacies of k-epsilon model is the over estimation of turbulent
kinetic energy however the slight improvement has been achieved after the development of
modified k-epsilon models.
2.2.2. Direct Numerical Simulation (DNS)Direct Numerical Simulation is used in computational fluid dynamics to solve the Navier-
Stoke equations numerically without any turbulence model. This means that the whole range
of spatial and temporal scales of the turbulence must be resolved. The power required to
resolve such models with current computational capabilities, makes them inappropriate for
large CDF applications. (Direct numerical simulation (DNS), 2007)
2.2.3. Large eddy simulation (LES)Large eddy simulation is a popular technique used for the simulation of turbulent flows.
This feature allows one to explicitly solve for the large eddies in a calculation and implicitly
account for the small eddies by using a subgrid-scale model (SGS model). (Large eddy
simulation (LES), 2007). The power requirement for LES is less than DNS but more than
RNS. The RANS methods give a time averaged result while LES methods are able to resolve
turbulent flow structures and predict instantaneous flow characteristics.
2.2.4. Detached eddy simulation (DES)It is the hybrid technique which combines the best aspects of RANS and LES
methodologies in a single solution strategy. There are some difficulties associated with the
use of the standard LES models, particularly in near-wall regions. These issues lead to the
development of hybrid models like DES. This model attempts to treat near-wall regions in a
RANS-like manner, and treat the rest of the flow in an LES-like manner. (Detached eddy
simulation (DES), 2007)
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2.3. Weibull distributionWindSim uses Weibull distribution to create a wind frequency table from met mast
information (Wallbank, 2008)
Figure 2 Sample output of energy module
3.Analysis3.1. Methodology
WindSim contains the following modules:
Terrain module
Establish the numerical model based on height and roughness data
Wind Fields module
Calculation of the numerical wind fields
Objects module
Place and process wind turbines and climatology data.
Results module
Analyse the numerical wind fields
Wind Resources module
Couple the numerical wind fields with climatology data by statistical means to provide the
wind resource map
Energy module
Couple the numerical wind fields with climatology data by statistical means to provide the
Annual Energy Production (AEP); including wake losses. Determine the windcharacteristics used for turbine loading. (WindSim, 2011)
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The terrain model generates a 3D model of the area under examination. Input includes
coordinates, height and roughness. A map is first converted using the terrain module. In
Refinement Type the Refinement area is detailed along with the number of cells to be used this
allows greater accuracy in computations for the chosen area. (WindSim, 2011) Resolutions in
the range 5000, 10000, 50000, 80000, 100000, 150000, 200000, 250000, 300000 will be
selected and the results recorded.
Cell resolution at 300000 and 5000 are shown below.
Figure 3 Cell resolution at 5000
Figure 4 Cell resolution at 300000
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The Objects module is used to specify each of the proposed turbines. The turbine models are
as follows:
Vestas V52 Ferdinand, 850 KW, hub height 65m
Vestas V52 Vilhelm, 850 KW, hub height 65m
NEG Micon 52, Freja, 900 KW, hub height 49m
Figure 5 Power curve Vestas V52 850
Figure 6 Power curve NEG Micon 52 900
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Figure 7 Objects as placed in terrain module
The Energy results for each increasing resolution will then be presented and discussed. A
wind resource map for the highest resolution will also be recorded.
3.1.1. Wake effectsThe WindSim wind resource model provides for the calculation of wake effects based on
analytical models (WindSim, 2011). In this report Model 1 has been chosen. This model is
based on momentum deficit theory and gives a simple linear expansion of the wake on the
basis of the wake factor, k.
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V = (1 - SQRT(1 - CT))/(1 + (2kx/D))2
Where:
CT = thrust coefficient (-)
k = A/LOG(h/z0)
A = 0.5
h = hub height (m)
z0 = roughness height (m)
(Source: WindSim.com)
3.1.2. Turbulence modelThe wind fields module allows for the selection of a Turbulence model. The default
model is the standard k- model belonging to the family of eddy viscosity models. An eddy
viscosity is calculated by an analytical equation (WindSim, 2011). The standard form of the
k- model is summarized as follows, with, t denoting differentiation with respect to time and,
i denoting differentiation with respect to distance:
k),t + ( Ui k - {t/PRT(k)} k,i ),i = (Pk - )
(),t + ( Ui - {t/PRT()} ,i ),i = {/k} (C1 Pk - C2 )
t = C k2/
Here k is the turbulent kinetic energy; is the dissipation rate; is the fluid density; t is the
turbulent kinematic viscosity. C,C1, C2, PRT(k), PRT() are the model constants.
(WindSim, 2011)
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4. Results4.1. Production according to vindstat.nu
The production data for NEG Micon 52 Freja is not available on vindstat.nu
Vestas V52 850 KW Hunflen Ferdinand 800
2009 2010
January 104097
February 64299 112608
March 151877 158710
April 125396
May 165342
June 114888
July 132393
August 141227
September 235166
October 156036
November 191045
December 92123
Figure 8 Yearly output 2009-2010 Ferdinand from vindstat.nu
Average yearly output Feb 2009Jan 2010 is 1673, 8 MW
Vestas V52 850KW Hunflen Vilhelm 801
2009 2010
January 98847
February 50779 87414
March 132320 142738
April 109980
May 107988June 92666
July 118927
August 125998
September 215377
October 141055
November 180530
December 87431
Figure 9 Yearly output Vilhelm 2009-2010 from vindstat.nu
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Average yearly output Feb 2009Jan 2010 is 1461,8 MW
4.2. WindSim Results4.2.1. Wake model 1
Frequency Table Power production in MWh/y for the differing cell resolutions based on
frequency table is presented below.
WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000
Ferdinand 1867,1 2003,7 2110,4 2152,8 2214,8 2236,3 2088,7 2241,3 2259,6
Vilhelm 1946,5 1995,7 2086,9 2164,5 1972,3 2088,9 1847,1 2089,8 1960,4
Freja 1337,7 1508,0 2036,0 2221,4 2098,2 2200,6 2012,2 2224,3 2101,4
Total 5151,3 5507,4 6233,3 6538,7 6285,3 6525,8 5948,0 6555,4 6321,4
Figure 10 Power output from WindSim frequency table
The table below shows the variation in estimated energy output across differing cell
resolutions.
Figure 11 Power output per turbine Frequency
The table below shows difference in actual production and forecast production for each of the
two turbines for which information is present on vindstat.nu.
Difference Ferdinand = Estimated production - Actual production 1673,8
Difference Vilhelm = Estimated productionActual production 1461,8
1000.0
1200.0
1400.0
1600.0
1800.0
2000.0
2200.0
2400.0
P
o
w
e
r
o
u
t
p
u
t
Cell Resolution
Frequency
ferdinand
wilhelm
freja
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Figure 12 Estimated production actual production Frequency table
WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000
Ferdinand 1867,1 2003,7 2110,4 2152,8 2214,8 2236,3 2088,7 2241,3 2259,6Actual 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9Difference 193,2 329,8 436,5 478,9 540,9 562,4 414,8 567,4 585,7
% 11,5426411 19,70328 26,07766 28,61068 32,31463 33,59906 24,78127 33,89777 34,99103
Figure 13 Actual vs estimated production frequency table
Weibull Distribution Power production in MWh/y for the differing cell resolutions based on
Wiebull distribution is presented below.
WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000
Ferdinand 1908,6 2045,3 2146,3 2198,0 2252,0 2280,8 2125,0 2284,3 2305,5Vilhelm 1986,7 2035,9 2125,2 2211,6 2010,3 2135,4 1885,7 2134,7 2006,6Freja 1375,1 1548,4 2077,8 2266,2 2139,2 2246,0 2053,5 2268,2 2145,7
Total 5270,4 5629,6 6349,3 6675,8 6401,5 6662,2 6064,2 6687,2 6457,8Figure 14 Power output from WindSim frequency table
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
po
w
e
r
o
u
t
p
u
t
Cell resolution
Difference between estimated and Actual
production Frequency table
Ferdinand
Vilhelm
WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000
Wilhelm 1946,5 1995,7 2086,9 2164,5 1972,3 2088,9 1847,1 2089,8 1960,4Actual 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9Difference 484,6 533,8 625,0 702,6 510,4 627,0 385,2 627,9 498,5% 33,1488243 36,51431 42,75278 48,06095 34,91365 42,88959 26,34944 42,95115 34,09964
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Figure 15 Power output per turbine Weibull distribution
The table below shows the variation in estimated energy output across differing cell
resolutions. The table below shows difference in actual production and forecast production for
each of the two turbines for which information is present on vindstat.nu.
Difference Ferdinand = Estimated production - Actual production 1673,8
Difference Vilhelm = Estimated productionActual production 1461,8
Figure 16 Estimated production actual production Weibull distribution
1000.0
1200.0
1400.0
1600.0
1800.02000.0
2200.0
2400.0
P
o
w
e
r
o
ut
p
u
t
Cell Resolution
Weibull distribution
Ferdinand
Wilhelm
Freja
0.0
200.0
400.0
600.0
800.0
1000.0
5000 10000 50000 80000 100000 150000 200000 250000 300000
P
o
w
e
r
o
u
t
p
u
t
Cell resolution
Difference estimated vs Actual production
Weibull distribution
Ferdinand
Vilhelm
Freja
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Figure 17 Actual vs estimated production frequency table
4.2.2. Wind Resources
WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000
Ferdinand 1908,6 2045,3 2146,3 2198,0 2252,0 2280,8 2125,0 2284,3 2305,5Actual 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9Difference 234,7 371,4 472,4 524,1 578,1 606,9 451,1 610,4 631,6
% 14,0218975 22,18851 28,22236 31,31098 34,537 36,25754 26,94988 36,46664 37,73315WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000Wilhelm 1986,7 2035,9 2125,2 2211,6 2010,3 2135,4 1885,7 2134,7 2006,6Actual 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9Difference 524,8 574,0 663,3 749,7 548,4 673,5 423,8 672,8 544,7% 35,8986742 39,26416 45,37266 51,28278 37,51301 46,07038 28,98985 46,0225 37,25992WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000Freja 1375,1 1548,4 2077,8 2266,2 2139,2 2246,0 2053,5 2268,2 2145,7Actual 1317,1 1317,1 1317,1 1317,1 1317,1 1317,1 1317,1 1317,1 1317,1Difference 58,0 231,3 760,7 949,1 822,1 928,9 736,4 951,1 828,6
% 4,40 17,56 57,76 72,06 62,42 70,53 55,91 72,21 62,91
Figure 18 Wind Resource map and Wind Rose at 300000 cell resolution
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Figure 19 Turbulence model comparison Ferdinand
Figure 20 Turbulence model comparison - Freja
1900.0
1950.0
2000.0
2050.0
2100.0
2150.0
2200.0
2250.0
2300.0
10000 100000 150000 200000 250000 300000
Po
w
e
r
o
u
t
p
u
t
Resolution
Comparison RNG with Standard and Modified
Turbulence models
Ferdinand
RNG
Ferdinand
Modifiied
Ferdinand
Standard
1400.0
1500.0
1600.0
1700.0
1800.0
1900.0
2000.0
2100.0
2200.0
2300.0
10000 100000 150000 200000 250000 300000
P
o
w
e
r
o
u
t
p
u
t
Resolution
Comparison RNG with Standard and
Modified Turbulence models
Freja RNG
Freja Mod
Freja
Standard
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Figure 21 Turbulence model comparison - Vilhelm
5. DiscussionThe number of simulations within the limited time frame may affect the validity of the
results obtained. The processing power available did not allow for production of energy
estimations for cell resolution in excess of 300000.
As production data for the NEG Micon Freja is unavailable discussion against actual
production will be limited to the above results and is perhaps best examined per turbine.
5.1. Vilhelm Vestas V52As cited above yearly power output based on vindstat.nu was 1461,8 MW. The nearest
result to actual production comes at 200000 cell resolution at an estimated production of
1847, 1 MWh/y for frequency table and 1885, 7 MWh/y for Weibull distribution. The power
estimation is next closest at 5000 cell resolution at 1946, 5 MWh/y and 1986,7 MWh/yrespectively. The results in the range 10000- 150000 cell resolution show a fluctuation in
power output as can be seen in Fig 11 and 14 above. At cell resolution 300000 the power
output decreases again and it is possible with further resolution it would have decreased
further.
5.2. Ferdinand Vestas V52As cited above yearly power output based on vindstat.nu was 173,8 MW. The nearest
result to actual production comes at 5000 cell resolution at an estimated production of 1867,1
1700.0
1750.0
1800.0
1850.0
1900.0
1950.0
2000.0
2050.0
2100.0
2150.0
2200.0
10000 100000 150000 200000 250000 300000
P
o
w
e
r
o
u
t
p
u
t
Resolution
Comparison RNG with Standard and
Modified Turbulence models
Vilhelm RNG
Vilhelm Mod
Vilhelm
standard
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MWh/y for frequency table and 1908,6 MWh/y for Weibull distribution. The power
estimation is next closest at 10000 cell resolution at 2003,7 MWh/y and 2045,3 MWh/y
respectively. The results in the range 50000- 250000 cell resolution show a fluctuation in
power output as can be seen in Fig 11 and 14 above. As opposed to the result for Vilhelm at
cell resolution 300000 the power output does not decrease again however it is possible with
further resolution it would have decreased.
5.3. Freja NEG Micon 52The energy estimation results for Freja show a very similar pattern to Vilhelm. However,
there is quite a marked jump in estimation from 5000 and 10000 cell resolutions producing a
very low estimate when compared with 50000 and beyond. There is little stability that can be
observed in the estimations with both frequency table and Weibull distribution generatingenergy estimates varying in size across the range of sampled resolutions.
6. ConclusionThe energy estimations from WindSim clearly overestimate the production from the
turbines as compared to actual production. As has been discussed in theoretical framework the
k-epsilon model has a tendency to over-estimate. The impact of availability may have a
significant impact on the difference in results along with the unavailability of simulations athigh resolution.
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Bibliography
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Appendices
Table 1. Vindstat data, 850 Vestas Hunflen Ferdinand 800
2005 2006 2007 2008 2009 2010 2011
January 135509 198817 291270 277887 267069 104097 232270
February 151846 145239 107846 241300 64299 112608 164087
March 64267 126711 150467 215211 151877 158710 264617
April 147311 154722 205126 115484 125396 140118 170173
May 254261 100726 206088 93358 165342 108958 173498
June 192459 152794 82501 135849 114888 102062 109826
July 246063 132559 141528 87003 132393 187878 86645
August 128883 90937 147009 118517 141227 127678 103911
September 167647 249708 87951 235166 160690 187234
October 149726 217889 244696 156036 212775 257853
November 294222 225500 201147 191045 202575 200503
December 349604 233641 151972 92123 132287
Table 2. Vindstat data, 850 Vestas Hunflen Vilhelm 800
2005 2006 2007 2008 2009 2010 2011
January 103766 188613 259690 279079 244542 98847 200899
February 131170 48898 100040 215324 50779 87414 145993
March 57522 16772 153524 192645 132320 142738 190854
April 115597 137374 181073 109201 109980 116687 130356
May 236364 103011 186266 82239 107988 94455 147528
June 176052 134896 81121 119988 92666 88379 99229
July 224016 116525 126854 82524 118927 158707 74223
August 169196 81255 137331 100446 125998 112743 92149
September 146726 202549 84835 215377 124641 169207
October 135108 70606 179583 141055 193865 233937November 239495 186387 190209 180530 183378 187747
December 306282 211737 118489 87431 119595