Streamtube Theories for Vertical Axis Wind Turbines Past, Present 1 [623869]

Streamtube Theories for Vertical Axis Wind Turbines – Past, Present 1
& Future 2
3
M Abdul Akbar*, V Mustafa 4
5
Department of Civil Engineering, Madanapalle Institute of Technology and Science, 6
Madanapalle, Chittoor District. Andhra Pradesh 517325 7
*[anonimizat] , [anonimizat] 8
9
ABSTRACT 10
11
Wind energy converters are classified as either horizontal-axis or vertical-axis based on the axis 12
around which it rotates. Numerous methods are available for the analysis of Vertical axis wind 13
turbines (VAWTs). The simplicity of streamtube theories despite its inaccuracies has made it the 14
most popular method for beginners working on the analysis of VAWTs. The basic theory behind 15
streamtube theories is the splitting of VAWT into different streamtubes and applying a trial and 16
error procedure for each to find out the induction factor that leads to the calculation of the overall 17
performance. 18
19
The paper provides a distilled summary of past four decades of streamtube theories since its first 20
introduction in 1974. It begins with a discussion of the evolution of streamtube theories from single 21
to double multiple approaches. It provides an outline of various new methods and approaches along 22
with innovations, primary application, and advanced applications which either directly or 23
indirectly use the streamtube theories. The paper discusses the historical perspective on the usage 24
trends; codes developed and reasons for choosing other methods with reference to the case by case 25
user application. It provides an outline of the future of streamtube theories based on the 26
contemporary usage and development trends. 27
28
Keywords : 29
Streamtube theory; Vertical Axis Wind Turbine; Blade Element Momentum; Double Multiple 30
Streamtube Theory; Single Streamtube; Multiple Streamtube 31
32
33
34
1. Introduction 35
36
Numerous methods have been proposed and used for solving the flow physics of Vertical axis 37
wind turbines (VAWTs). Out of all the methods, solutions based on streamtube theories stands 38
out. The easiness of the approach makes up for the inaccuracies, a strong testimony of which is 39
evident from the numerous codes that are either directly or indirectly based on streamtube theories. 40
Table 1 lists some such codes developed with a brief description and the type of streamtube theory 41
they utilize. 42

43
Code Theory Brief Description Ref.
BEMT DM MATLAB based code maintaining non-dimensionality of the
BE-M approach. Includes wake effect and dynamic stall
calculation by various proposed models [26]
CARDAA DM First program based on Double Multiple Streamtube Theory
(DMST) with its initial developments [5]
CARDAAS DM Takes into account the fluctuating nature of the wind [29]
CARDAAV DM Several shapes like catenary, troposkien, sandia & parabola can
be analyzed. Accounts for secondary effects due to struts,
spoilers & rotating central tower [14]
CARDAAX DM Takes into account the streamtube expansion [29]
CMDMS DM The airflow is split into two parts – Overall & local. The
description of blade profile in the local part is in the form of a
circle using conformal mapping [13]
CODIF DM Same as SIDIF except that the reference rotational angle is
turned by 900 to enable a Cosine distribution interference factor [10]
DART M Among the first codes based on streamtube theories when they
were still under development [1, 2]
DARTER M Modification of DART using airfoil data based on elemental
Reynolds numbers and more blade shapes [2, 3]
DMSM-FEC DM Incorporates flow expansion corrections [28]
DMSV DM DMST with angular dependency of the interference factor [28]
EB-DMSM DM Energy based model that employs tangential force coefficient
for calculating interference factor [28]
FFEVD DM Is a preprocessor code for the FEM-based NASTRAN.
Aerodynamic loads are computed using DMST. [18]
FloVAWT DM Time-domain based analytical tool for offshore VAWTs which
uses DMST for aerodynamic calculation [27]
FORCE S Assessment of aerodynamic blade loads [6]
FRAST DM Model incorporating aero elastic effects in FFEVD [18]
FWAEROLD DM A FORTRAN based code that is a modified version of FORCE
algorithm developed by Sandia [11]
LDWT M Considers the value of local Reynolds number instead of the
overall Reynolds number [24]
MB-DMSM DM Differs from EB-DMSM in that it uses streamwise force
coefficients for calculating interference factor [28]
MDMSM-FEC DM Modified DMS model with flow expansion correction [28]
MDMSM-NFE DM Modified DMS model with no flow expansion [28]
MDMSM-
WFE DM Modified DMS model with flow expansion [28]
MSM-FEC M Modified multiple streamtube modeling with flow expansion
correction [28]
PAREP M Combines theory with results of wind-tunnel testing to better
represent the overall aerodynamic performance. [2,
335]

pyDART M A modified version of Strickland’s FORTRAN based DART re-
written in the programming language, Python to take
advantages of object -oriented programming [16]
QBlade DM Most popular open source code based on DMST for
comprehensive analysis, design & optimization of VAWTs.
Integrated with XFLR5 for lift & drag data [22,
23]
SIDIF DM Modeling of velocity decrease that occurs as the wind passes
through the VAWT as a sinusoidal function including the
dynamic stall effects [8]
SIMOSS S Based on single streamtube that can handle parabolic, straight
and trapezoidal blade shapes [2]
SLICEIT DM Based on steady state wind modeling which uses Gormont
dynamic stall model [9]
STOCH_3D DM The 3-D effects of wind turbulence are taken into consideration
and modeling of loading on the blades by a combination of
actuator disc theory and strip theory [18]
StrathDMS DM MATLAB based code for variable pitch VAWTs [20,
21]
TRES4D DM The effect of turbulence of wind is taken into account [18]
VAPE S Made for a unconventionally shaped VAWT, which is
cylindrically pitched and has three straight blades. Dynamic
stall included [4]
VARDAR DM Takes into account the skewed flow of wind as experienced by
VAWTs installed on roof tops [17]
VAWT DM To predict the steady state response of a cyclo-turbine with
fixed or self -acting variable pitch straight -blades [12]
VAWT_DYN DM Same as VAWT but used for dynamic response prediction [12]
VAWTEX -B DM Models the effect of variable pitch hydrokinetic turbines [19]
VAWTGUI M &
DM Development of a tool based on MATLAB with interactive
Graphical user interface for application to irregular geometries
and wind profiles [15]
VAWTTAY6 M To analyze the Taylor ‘V’ Type VAWT. Takes into account the
blade inclination, blade shape, blade taper, blade pitch and
tangential blade offset [7]
W.O.M.B.A.T M &
DM New generation code for optimization of VAWTs that uses
genetic algorithm & can impose multiple objectives [25]
Table. 1: List of codes developed based on streamtube theories (S – Single, M – Multiple, DM – 44
Double Multiple) 45
46
The technical term streamtube in its traditional definition has been used even before [30] the 47
introduction of classical streamtube theories in 1974. It is still being used [31, 32] and is also used 48
in other allied fields which involve fluids of other types like water [33]. 49
50
Much of the initial development of the streamtube theories happened in Canada through National 51
Research Council (NRC) and in the United States through Sandia National Laboratories (SNL). 52
These neighboring countries through their combined effort developed the theory with validations 53

mostly based on Darrieus VAWTs. The early researchers who were instrumental in laying the 54
foundations of the theory were well-known figures within themselves who used to meet during 55
numerous workshops held during the 1970’s at a time when the World Wide Web and fast 56
dissemination of knowledge were not in the best frame of things. Even to this day, a lot of papers 57
that bring out novel ideas based on streamtube theories are from researchers based in Canada. This 58
“Past, Present & Future” paper summarizes all the key points during the four decades of streamtube 59
theories. Based on the developments, a projection into the future of streamtube theories is also 60
discussed. 61
62
2. Theoretical Foundations 63
64
The classical streamtube theories have gone through an immense transformation through the years. 65
Out of these transformations, three phases are the most prominent ones and is often referred to in 66
discussions about the history of streamtube theories. They are the transformation from ‘Single 67
streamtube theory’ to ‘Multiple streamtube theory’ to ‘Double multiple streamtube theory’ 68
(DMST). Fig. 1 shows a simple representation of these phases. There is also an intermediate stage 69
with single streamtube and double disk approach. However, it is not included in the figure as the 70
history of streamtube model developments were centered on the given three models. 71
72
73
Fig.1. Evolution of stream tube theory; (a) – Single streamtube theory, (b) – Multiple streamtube 74
theory, (c) – Double multiple streamtube theory 75
This section through its subsections covers the development of the streamtube theories. The 76
findings described in this section have been listed roughly in the chronological order of their 77
occurrence so as to enable a story type description that would entice the reader to the natural flow 78
of events. 79
80
81
82
83

2.1 The beginnings 84
85
The first reference to the classical streamtube theories was by Templin [34] in the year 1974 with 86
the introduction of the single streamtube theory as an “Aerodynamic Performance Theory” for 87
NRC VAWTs. The effects of aerodynamic stall and curvature of the blade on performance was 88
incorporated. In the same year, Robert et al. [35] in a report with a primary focus on HAWTs 89
introduced the concept of using multiple independent streamtubes for analysis. The streamtube 90
models gained further momentum when James on behalf of SNL wrote a report in 1975 [36] 91
comparing the single and multiple streamtube models with experimental results. The report 92
confirmed better prediction capabilities of multiple streamtube models when compared to single 93
streamtube models for small rotors. Lapin [37] briefly introduced the concept similar to DMST of 94
having two actuator disks in tandem in 1975 when he developed it to study the economic feasibility 95
of a large rotor. His concept of having “actuator disks” in tandem went largely unnoticed at that 96
time, and research works continued focus on single and multiple streamtube theories. 97
98
99
Ralph et al. [38] introduced a complete approach to streamtube models to include the effects of 100
support struts, airfoil geometry, blade aspect ratio, windmill solidity, blade interference and 101
curvature of flow in the analysis. One of the earliest known Maters level theses based on 102
streamtube theories was by Gopal [39] in 1976 who worked under Strickland, which included 103
studies on the effect of aspect ratio and blade solidity on Darrieus VAWT performance. Qualitative 104
comparison of streamtube theories with results obtained from wind tunnel testing was done [40, 105
41] for commercial and SNL VAWTs. The quarterly reports of SNL for Oct – Dec 1975 [42] and 106
April – June 1976 [334], demonstrated the application of streamtube theories for performance 107
prediction of large Darrieus rotors (5m and 17m). Strickland’s [1, 43] multiple streamtube model 108
was inclusive of factors such as blade taper, atmospheric wind shear induced spatial variation, 109
Reynolds number effects for large rotors, etc. One of the earliest known patents that allude to the 110
fundamental concepts of Momentum theory was by Gaston Bourquardez [44] in 1977. A state-of- 111
the-art article that comprehensively summarizes the initial stages of the development of streamtube 112
theories was written by D G Shepherd [45] in 1978. 113
114
2.2 Theorem solidification & worldwide acceptance 115
116
Around the same time, across the globe in India, some research activities were going on in National 117
Aeronautical Laboratory (NAL) on the Darrieus VAWTs [46] following the revival of the concept 118
at NRC, Canada. Field measurements of a 5 meters tall Darrieus VAWT build using wooden blades 119
compared well with the predictions of the streamtube theories [46]. The streamtube formulations 120
were modified to consider the effects of strut drag, turbulent wake state, and dynamic stall for 121
application to a straight-bladed but cyclically pitched VAWT by Noll et al. [4]. A more 122
comprehensive formulation of the streamtube theories introduced by Read et al. [47] gained 123
acceptability owing to its amenability to computer programming to include effects of turbine 124
specific parameters. 125
126
Despite the simplicity of streamtube theories, a real constraint of the methods (which exists even 127
today) is the requirement of lift and drag coefficients for the aerofoil and the Reynolds number 128
under consideration [52, 53, 196, 295] . As a lot of initial researches on airfoils were primarily in 129

the aerospace industry, the available database of lift and drag coefficients were for Reynolds 130
numbers that were much higher than that experienced by VAWTs. Identifying this void, SNL 131
conducted extensive wind tunnel testing for symmetrical NACA aerofoils and documented these 132
coefficients for a range of angle of attacks and Reynolds numbers starting from 10,000 [54]. Fig. 133
2 shows the plot of NACA symmetrical aerofoils for which force coefficient data are available in 134
the tabulated format in [54]. Numerous low Reynolds number experimental data [55 – 60] have 135
been documented through the efforts of UIUC low-speed airfoil tests. However, the 136
comprehensiveness of the SNL report [54] and the simplicity and reproducibility of symmetrical 137
NACA aerofoils has made it the most referenced database for research activities on VAWTs and 138
related fields even to this day [61 – 64]. 139
140
Fig. 2. NACA symmetrical aerofoils with tabulated force coefficient data in [54] 141
142
143
The confidence on streamtube theories grew among SNL researchers with its application of being 144
a part of the comprehensive analysis package for their 17–m research turbine [48]. Despite the 145
relative success, some severe limitations of the streamtubes theories surfaced. Sullivan in his 146
assessment of all methods including streamtube theory developed for structural calculations 147
described them as workable but immature [6]. He stated that this immaturity was from the 148
uncertain effects of the approximations built into the design tools. A need for streamtube theories 149
to differentiate between upstream and downstream cycles was apparent through findings of Wilson 150
[49] who pointed out the inherent deficiency of streamtube theories in predicting the wake based 151
angle of attack difference for the upstream and downstream cycles of the rotor. 152
153
2.3 Introduction of DMST 154
155
The time for the introduction of DMST was ripe and the Second DOE/NASA Wind Turbine 156
Dynamics Workshop held in Cleveland, Ohio during the following year (1981) marked a new 157
chapter in the history of streamtube theories. The DMST was formally introduced to the scientific 158
world by Paraschivoiu [5] during the workshop. DMST treated the upstream and downstream 159 -0.13-0.08-0.030.020.070.120.17
0.0 0.2 0.4 0.6 0.8 1.0NACA 0012
NACA 0015
NACA 0018
NACA 0021
NACA 0025

halves of the VAWT separately and as a consequence the wind was required to pass through two 160
actuator disks in tandem before reaching the other end. Paraschivoiu was also able to demonstrate 161
the improved accuracy achieved with DMST when compared with earlier streamtube models. The 162
workshop also featured a paper on the dynamic analysis of Darrieus VAWTs, which used a single 163
streamtube theory [50] and a paper on fixed wake model for analysis of darrieus VAWTs using 164
multiple streamtube theory [51]. Klimas, who was a participant in the workshop, presented a paper 165
on Darrieus VAWT experimental activities at SNL [65]. In the following year, Klimas in his report 166
on Darrieus rotor aerodynamics [66] observed that the progression of streamtube models from 167
single to DMST has certainly improved the prediction capacity of VAWTs, but more work needs 168
to be done to represent exactly non-symmetric blade sections and blade section behavior in the 169
dynamic, curvilinear environment. 170
171
2.4 Refined models of DMST & tackling dynamic stall 172
173
Berg [10] modified the DMST model to incorporate the effects of the incident wind boundary 174
layer, non-uniform velocity between the upwind and downwind sections of the rotor, dynamic stall 175
effects and local blade Reynolds number variations. Paraschivoiu’s contributions to DMST 176
continued in the subsequent years with many co-authored papers [67 – 70]. Paraschivoiu et al. [67] 177
introduced a new formulation for an approximate troposkien shape by considering the effect of the 178
gravitational field. Studies on the effects of three NACA symmetrical profiles namely; 0012, 0015 179
and 0018 on the aerodynamic performance of the turbine led to the development of a semi-180
empirical dynamic stall model. Paraschivoiu et al. [68] modified DMST to include the secondary 181
effects namely the blade geometry and profile type, the rotating tower and the presence of struts 182
and aerodynamic spoilers. Paraschivoiu [69] modified DMST model for Darrieus wind turbines 183
with straight and curved blades to account for the effects of streamtube expansion and dynamic 184
stall. Paraschivoiu [70] modified DMST model to incorporate the effects of dynamic stall and 185
secondary effects and subsequent transfer of loads for structural design. Amos et al. [232] 186
improved the existing DMST formulations to include the effect of instantaneously changing 187
Reynolds number to use the most appropriate lift and drag coefficients. In 1986, Templin who is 188
the founder of streamtube theories summarized the various aerodynamic models of the past decade 189
for the analysis of Darrieus VAWTs [71]. He concluded that in general all the methods provide 190
satisfactory accuracy overall but differs in their prediction of detailed blade load distributions. 191
192
193
2.5 Stabilization of DMST & challenges remaining 194
195
The SNL activists had significantly enabled the growth of streamtube theories as their experiments 196
on Darrieus VAWTs of various sizes (2-m, 5-m, 17-m, 34-m, etc.) provided ample amount of field 197
data against which the predictions of streamtube models were verifiable. However, SNL concluded 198
their research activities on Darrieus VAWTs and VAWTs in general by mid-1990’s [72]. Also 199
around this time, the theoretical formulations of DMST have more or less stabilized in a way that 200
a major overhaul was not required. Nevertheless, research activities on the poor accuracy of DMST 201
for high tip speed ratio and high solidities continued through the years. The focus of much of the 202
research activities in the years leading to 2000 were on accurately quantifying the dynamic stall 203
coefficients of different aerofoils [73] as DMST unlike other more accurate methods require these 204
values as input to carry out its computations. In the absence of dynamic stall data for the aerofoil 205

under consideration, the standard practice was to perform calculations assuming there is no 206
dynamic stall that in reality is valid only for large tip speed ratio’s (approximately > 5) [74 – 76]. 207
Otherwise, some active dynamic stall controlling devices like the use of synthetic jets as presented 208
by Joshua et al. [77] needs to be in place for the assumption to be valid. 209
210
Bent Sorensen [78] covered a general discussion on cross-wind and other alternative converter 211
concepts and the finer details related to their momentum modeling approaches. Carlos [79] 212
examined the DMST model critically given two-dimensional and three-dimensional wake 213
experienced by the VAWTs. He proposed a correction to the existing DMST based on his wake 214
modeling. Despite his corrections, he noted that the limitations of DMST with regards to accurately 215
capturing the effects of wake were still prevalent. Simao et al. [291] through comparison with other 216
codes explored the deficiency of the streamtube theories modeling issues on modeling of wake 217
phenomenon. 218
219
3. New Findings, Ideas & Approaches 220
221
The streamtube theories have directly or indirectly led to a lot of new findings, ideas & approaches 222
that have helped to understand better the VAWT flow physics. Some of these results were useful 223
for other methods whereas some finding were useful for streamtube theories itself not just from an 224
accuracy point of view but also in reducing the computational effort. This section discusses the 225
highlights of such significant developments. A classification of the works based on the various 226
categories to which they belong provides a meaningful insight. The works reported in this section 227
is discussed under five subsections. 228
229
3.1 New theoretical formulations 230
231
In 1976, Wilson [80] introduced a strip theory in which the time-averaged force on a blade element 232
equated to the mean momentum flux through a streamtube of fixed location and dimensions. The 233
multiple streamtube approach was used by Paul [84] in tracking wind turbulence as it passes 234
through the rotor. An indirect method aided in the characterization of the performance of Natural 235
Laminar Flow (NLF) aerofoil’s based on the cost-of-energy (COE) approach of artificial VAWTs 236
modeled using DMST [85]. Malcolm [88] in his studies on the dynamic response of darrieus 237
VAWTs subjected to turbulent flows used DMST in generating time series vectors of longitudinal 238
and lateral turbulent velocities. Inseung et al. [97] employed DMST analysis to analyze a 5-bladed 239
VAWT with slanted blades of rake angle 300. Basic trigonometry based on the angular position 240
of the blade was used to arrive at modifications for the DMST formulations. Paraschivoiu et al. 241
[14] proposed a procedure for computing the optimal variation of the blades pitch angle of a 242
straight bladed VAWT that maximizes its torque at given operational conditions. 243
Isaac et al. [105] presented a new computational model for initial sizing and performance 244
prediction of VAWTs. Raciti et al. [113] proposed an analytical model for the evaluation of the 245
energy efficiency and distribution of aerodynamic forces acting on a Darrieus VAWT depending 246
on both rotor architecture and operating conditions. The model uses all levels of streamtube 247
theories starting from single streamtube to DMST. Kevin et al. [123] proposed a new approximate 248
streamtube method to predict the momentum, lift, and drag forces on the rotor surfaces of a 249
Savonius type VAWT by the air stream through an integral force balance on the turbine blades. 250
Conaill [21] developed a DMST aerodynamic evaluation tool that can model any piecewise linear 251

blade VAWT rotor configuration and variable pitch regimes. Hara et al. [127] developed a 252
quadruple-multiple streamtube model for double bladed VAWTs and butterfly shaped VAWTs 253
wherein the wind would be required to pass the blade twice during upwind and downwind cycles. 254
Argen et al. [190] introduced a solution based on conformal mapping of the wing sections to circles 255
for solving the two-dimensional and time-dependent potential flow. A double step momentum 256
model used to simulate the aerodynamics of VAWTs by splitting it into the overall flow part, and 257
the local flow part [13, 191, 192] demonstrate the application of this approach. Timm [195] 258
introduced a new method for calculation of the optimum pitch angle that can maximize efficiency. 259
260
3.2 New approaches 261
Liao Kangping et al. [102] applied the reverse methodology of correcting the DMST algorithm for 262
dynamic stall effects in the low tip-speed ratio region and the secondary effects of the high tip-263
speed ratio based on the findings obtained from on field testing of VAWTs. Sumei et al. [108] 264
proposed an improved method to counter the divergent phenomenon of DMST induced by the 265
width characteristics of the streamtubes. The corrections were incorporated based on the findings 266
on a synchronous variable-pitch VAWT. With due consideration to both dynamic stall and 267
dynamic inflow phenomenon, a BE-M based method has evolved [112]. In this method, a number 268
of extra blades referred to as “ghost” blades are defined about the rotor azimuth, in addition to the 269
real blades. The method eliminates iteration and potential numerical instability in the induced 270
velocity calculation. Rafael et al. [119] in his paper on Integral analysis of rotors deals with a new 271
approach based on the modification of momentum principle. Matrawy et al. [216] studied the effect 272
of flaps in VAWTs using experiments and numerical modeling based on single streamtube 273
approach and observed better performance when compared to the case where there no flaps. Can 274
et al. [294] in a study that involved experimentation along with numerical modeling separates out 275
the predictions of the DMST with regards to the upstream and downstream and verifies it with 276
advanced experimental set up that uses Laser Doppler Velocimeter (LDV) probe and multi-point 277
pressure devices. 278
279
3.3 Core mathematical formulations 280
281
William [87] introduced an approximate method of analysis based on trigonometry of small angles 282
which is valid for Darrieus VAWTs up to six blades. Ladopoulos [96] presented an approach for 283
solving the nonlinear, unsteady problem of VAWT using integral calculus based on Green's 284
theorem. The problem is first investigated around the airfoil and extended to the blades by 285
assuming linear source distribution. The method does not use streamtube theories but similar to 286
the distinction made between upwind and downwind sides in DMST, the problem is studied using 287
two different approaches. The initial study uses the linear source distribution on the left-hand side 288
of the separating wake and the subsequent study with a positioning of the wake on the right-hand 289
side. Tamas et al. [100] introduced a new method referred to as "streamtube surgery" that combines 290
a variation of the multiple streamtube approach with a method capable of modeling flow field 291
interactions. This method can be used to explore the instantaneous and cycle-averaged flowfields 292
for VAWTs. 293
294

In 2009, Farthing [104] outlined a vector based mathematical approach to formulating a Blade 295
Element Momentum (BE-M) based vector double pass model as is done for Horizontal axis wind 296
turbines (HAWTs) to solve two and three dimensional VAWTs. Verkinderen et al. [129] in a 297
unique study of its kind presented a simplified dynamic model for mast design of H-type Darrieus 298
VAWT which used multiple streamtube modeling of aerodynamic loads. Esteban et al. [130] 299
derived analytical estimates to bound blade – wake interactions validated using a high order 300
discontinuous Galerkin solver that can be used to modify BE-M formulations. Esteban et al. [131] 301
also presented a paper on analytical estimates for various flow scales encountered in cross-flow 302
turbines which could be useful for BE-M based models. Good quality post-stall aerofoil force data 303
at low Reynolds numbers is essential for the analysis using streamtube formulations. Rainbird et 304
al. [132] presented a relationship between peak magnitude of post-stall lift and drag values and 305
blockage for conventional wind tunnel data that remains even after the application of corrections. 306
Rainbird et al. [133] used discontinuous Galerkin solver and BE-M code to stimulate the blade 307
wake interactions of a VAWT. 308
309
3.4 New findings 310
311
Newman [81 – 83] proved that by considering a large number of discs in the DMST analysis of 312
VAWTs, the maximum power coefficient obtained was 13% greater than the Betz limit of 0.593. 313
Application of streamtube theories to stochastic loads continued with efforts from researchers like 314
Gregory [93, 94] who used a DMST model that included the effect of wind shear to established 315
that the stochastic loads produced by atmospheric turbulence have a significant impact on average 316
output power. The previous estimates of the magnitude of the effects were proven to be 317
conservative. Lian et al. [101] using the multiple streamtube modeling established that the use of 318
local Reynolds number based on local relative velocity yielded better aerodynamic results than 319
using global Reynolds number. Jang-Ho Lee, who was a co-author of the paper, was also part of a 320
2013 paper [24] published in ‘Renewable Energy’ which sustained the findings of [101] with more 321
insight into the technical aspects. 322
323
Merim et al. [106] carried out unsteady 2-D and 3-D aerodynamical modeling of 2 bladed VAWT 324
with NACA 4418 airfoil. The study throws light on dynamic stall aspects of DMST formulations 325
that need rectification for the particular airfoil. Francisc et al. [126] Used the streamtube models 326
and lessons from early researchers in arriving at some considerations for use in computer-based 327
models for H-type Darrieus VAWTs suitable for small power applications. Brusca et al. [128] 328
through his work analyzed the link between the aspect ratio and Reynolds Number of operation of 329
an H-Rotor VAWT and its performance. 330
331
3.5 Developments beneficial for streamtube theories 332
333
Simon [86] presented an analytical model based on multiple streamtube theory to predict the 334
performance of curved bladed Darrieus VAWTs. The model predicts the dynamic stall point 335
accurately for Reynolds number of 28,000 without artificially altering the lift & drag data obtained 336
experimentally. A weak point of the streamtube iterations was the limit of induction factor while 337

using the Ideal thrust coefficient given (CT) by equation (1) for values of induction factor (a) above 338
0.4. 339
340
CT = 4∗a∗(1−a) (1) 341
342
The usage of Glauert’s approximation [89] of CT for induction factor (a) values above 0.4 given 343
by equation (2) resolve the issue. 344
345
CT = 0.889−0.444∗a+1.556∗aଶ (2) 346
347
This approximation originally proposed by Glauert [90] finds application for cases where the 348
induction factor (a) crosses the limit of validity of the ideal thrust coefficient [91, 92]. A graphical 349
comparison of the thrust coefficient using both approximations plotted with a resolution of 0.01 350
for the induction factor is shown in fig. 3. 351
352
353
Fig. 3. A comparison of Glauert’s thrust coefficient with the Ideal thrust coefficient 354
Despite its simplicity, one of the major drawbacks of the streamtube theories is the requirement of 355
an iterative trial and error procedure to arrive at the correct induction factor. Being a purely 356
mathematical subject, a deeper study of these aspects elude the traditional researcher working on 357
VAWT aerodynamics. However, the studies carried out by Alireza et al. [98] discusses this issue 358
in detail and suggests steps that can be taken to ensure a faster convergence of the induction factor. 359
This study has gained acceptance, and the findings have been part of QBlade [99]. McIntosh et al. 360
[103] discuss the convergence issue of the iterative procedure of streamtube theories concerning 361
the influence of partial stall, deep stall and dynamic stall in general on the convergence and the 362
concept of multiple roots for the iterative equation. The paper also discusses a geometric method 363
that comes handy in place of the iterative scheme for arriving at the value of induction factor. The 364
method has been used by Conaill et al. [111]. 365
366 00.20.40.60.811.21.41.61.82
0 0.2 0.4 0.6 0.8 1Thrust coefficient
Induction factorIdeal thrust coefficient
Glauert's approximation

Gabriele et al. introduced a dynamic stall-corrected BE-M algorithm using a hybrid database with 367
validations through the numerical comparison with Sandia experimental measurements on a 368
Troposkien shaped VAWT of height 2 meters [109] and 5 meters [110]. The DMST model 369
developed incorporated a new correction factor to account for strut drag effects. With the increased 370
computation capacities, a new trend has been to consider the fundamental aspects in the design of 371
VAWT like the inclination of the blade section, skewness of the wind, etc. into a more 372
programmable and whole approach. Such approaches were used by Moti [115], Batista et al. [116, 373
117] and Abdul et al. [118]. Fig. 5 shows the 3-D approach envisioned by Abdul et al. [118] for a 374
complex shaped VAWT. 375
376
377
378
Fig. 4. Three-dimensional generalization of DMST for complex shaped VAWTs 379
380
Richard [28] developed variations of the DMST model for Darrieus SB-VAWTs that are capable 381
of incorporating the effects of flow expansion. The correction of the BE-M code for its inability to 382
account for wake effects accurately was carried out based on the difference in the results obtained 383
for the downstream half of the rotor (where blade-wake was prevalent). Wang et al. [134] in his 384
study on offshore floating VAWT’s where the pitch motion would be significant, proposed a 385
modified form of the DMST equations to include the effect of the component of wind speed 386

parallel to the rotating shaft. Bogățeanu [193] and Bogățeanu et al. [194] included gust in their 387
formulations to study its impact on momentum model formulations. Mojtaba et al. [217] presented 388
a design procedure in the form of an algorithm that would be useful for industrial and research 389
purposes in determining the construction parameters of the VAWT prototype. 390
391
392
3.6 Combination of methods 393
394
The combination of streamtube models with other methods of analysis finds application in a wide 395
variety of scenarios. Abdel Azim et al. [95] developed a computing package that combines the 396
structural aspects and aerodynamic aspects considering the dynamic stall and dynamic aspects of 397
the response. The results of a Darrieus VAWT named PIONEER I built by Fokker company based 398
in Netherlands was a means for validation of the software. Marco et al. [107] combined BE-M 399
with Computational fluid dynamics (CFD) code to develop a design and optimization tool for 400
VAWTs. Mazharul et al. [114] developed a new code by combining the momentum and cascade 401
theories and used it to compare a series of low Reynolds number airfoils for application in smaller 402
capacity fixed-pitch straight bladed VAWT (SB-VAWT). A coupling method between a 403
streamtube model and the ONERA-EDLIN model has been implemented successfully to model 404
the performance of a Darrieus-like water turbine with active pitch variation [120]. 405
406
Marsh et al. [124] used DMST and CFD to investigate the power generated and calculate the 407
hydrodynamic properties of offshore VAWTs numerically. Yang et al. [125] developed a new 408
program using the combination of single streamtube and vortex method for the simulation of SB-409
VAWT. Naoko et al. [196] used the lift and drag values computed using CFD as the inputs for the 410
streamtube theories used for performance prediction. Chen [197] combined lifting line theory and 411
a modified DMST with Viterna & Corregian adaptation of dynamic stall to investigate the 3-412
dimensional effect on DMST. Elhadji et al. [198] used a three-pronged approach for modeling an 413
existing VAWT system for which reliable field data is available. This method involved the use of 414
CFD and DMST. 415
416
417
3.7 Genetic algorithm 418
419
The latest advancement of streamtube theories is the use of the genetic algorithm in computations. 420
Gabriele et al. [25] using a multi-objective genetic algorithm code discussed the procedure for 421
generation of an extensive database (lift & drag) of symmetric profiles and validated it with the 422
aim of adopting numerical optimization methods for VAWT design. Gabriele et al. [121] continued 423
the use of the genetic algorithm to arrive at an innovative chord distribution in the Troposkien 424
VAWT. The studies were substantiated, and they used the algorithm to attain the optimal spanwise 425
chord and thickness distribution for a Troposkien Darrieus VAWT [122]. Mauri et al. [170] used 426
the genetic algorithm for the design of a 3×3m (diameter/height) pitch-controlled lift based H-427
Darrieus VAWT for urban installations. 428
429
430
4. Innovations 431
432

Streamtube theories have been part of numerous innovatively shaped VAWTs and novel idea 433
either as a verification tool or as a direct consequence of the analysis results. The section deals 434
with a summary of some such innovations which has shaped the revival of the VAWT concept. 435
436
4.1 Innovative VAWT shapes 437
Table 2 lists some of the creative shapes that used the streamtube theories with a brief description 438
of them. Out of these, specific studies like that of papers co-authored by Fernando [136 – 141] on 439
the concept of Variable Geometry Oval Trajectory (VGOT) stand out not just from the uniqueness 440
of shape but also from new insights developed through formulaic modification of traditional 441
DMST formulations to suit the new model. The formulations included the effects of variable blade-442
positioning angle, the trajectory shape coefficient, and the wind orientation angle. Frédérick et al. 443
[218 – 224] patented the fluid directing system and Frédérick [225 – 231] patented the annular 444
multi-rotor double-walled turbine. Both of these inventions indirectly use DMST formulations 445
through the use of CARDAAV code. 446
447
Name Theory Brief Description Ref.
Taylor ‘V’ Type M 2 to 3 straight blades mounted in the form of a ‘V’ on a short
tower and supported by bracing cables from a central pylon [7]
Taylor ‘V’ Type
(Model-B) M Blades inclined at 45 degrees to the vertical by a pair of
cables. Moveable tip portion with adjustable pitch angle [7]
PIONEER I DM 15 m high Darrieus type VAWT with the turbine tower and
rotor tube made of two steel tubes of different dimensions.
Blade section made of GFRP skins and polyurethane core [95]
VGOT DM In Variable-Geometry Oval-Trajectory model, each blade
slides over rails mounted on a wagon formed by a reticulated
truss type structure supported by standard train bogies [136 –
141]
– S 4 or 5 bladed Vertical axis tidal turbine with oscillating
blades, similar to the Voith-Schneider system with blades
protruding under a disk rotating [142]
– M A novel VAWT built for educational purposes. The blades of
the turbine rotor are symmetric about their mid-chord and
rotate 180ș about this point for every complete revolution. [143]
KOBOLD DM The self-acting variable pitch type patented tidal turbine with
specially designed aerofoil that are cavitation free and have
high lift performance [12]
– DM A 5-bladed ruled surface VAWT with slanted blades of rake
angle 30 degrees [97]
Crossflex DM Building integrated wind turbine system developed for urban
conditions. Technically innovative, flexible blade system. Has
a lightweight cowling system for augmen ted airflow [152]
NOVA DM Offshore VAWT with sails attached to the arm to minimize
peak overturning moment resulting from cyclic blade forces to
reduce support structure and drive train stresses [162,
163]

SF750K-A – Double H-Type VAWT, which is patented by FengFa
technology. Improved self-starting ability and enhanced
stability of structure intensity [164]
– S/D/D
M Patented VAWT with geometry similar to troposkein. Chord
length and thickness to chord ratio varying continuously along
the length of the blade [166,
167]
– S/D/D
M Minimum chord length at the ends, second minimum at mid
height. Minimum value of thickness to chord ratio at the ends
and maximum value at mid -height [168,
169]
DB-VAWT QM Double Bladed VAWT in which two blades are placed close
to each other for improved self -starting performance [127]
BWT QM Has a butterfly shape as it rotates. Higher energy efficiency,
good self-starting performance and better vibration handling [127]
– DM 3×3m (diameter X height) pitch-controlled lift based H-
Darrieus VAWT for urban installations [170]
– DM A novel design for pitch control and actuation system
achieved by splitting the blade into two identical segments
with upper and lower sets of blades equipped with a single
actuation system [174]
– DM Darrieus VAWT with self-start ability due to an innovative
profile design named EN0005 that avoids the need for extra
components or external electricity feed -in [175]
Cylindrical G
HT S Tidal turbines designed for installation in free flow conditions
with blades fixed at approximately quarter -chord [176]
LST S Tidal turbine with varying chord, thickness, and camber along
their height designed for installation in circular cross -section’s [176]
CT-SBVAWT M Combines a two-stage Savonius rotor with a three-fan straight
bladed Darrieus rotor through an overrun clutch [199]
ZVWT S/M Zephyr is a type of savonius VAWT with stator veins. Ideal
when wind direction and velocity are constantly changing [200]
(Low-cost
VAWT options) M Bicycle wind turbine, biplane flexible-vane model, CPVC
pipe model, slanted model with composite blades. [203]
DeepWind DM Offshore VAWT with blade shape similar to the Troposkien
geometry but asymmetric between the top and bottom parts [214,
215]
Gorlov DM Helical-shaped tidal turbine that can reduce the effect of
“torque ripple” [257]
Table. 2: Innovative VAT (wind & tidal) shapes developed (S – Single, M – Multiple, DM – 448
Double Multiple, QM – Quadruple Multiple) 449
450
Daniel [153 – 160] presented a patented wind turbine concept that is capable of harvesting both 451
horizontal and vertical wind currents having an open frame structure and a central passage through 452
the structure. The open frame structure includes a unique rod and cable central structure offset 453
from the periphery of the frame. The author did not explicitly mention the usage of the streamtube 454
theories for its analysis but specified it as a possible tool for analysis. 455

4.2 Innovative Airfoil concepts 456
Binyamin et al. [144, 145] and Binyamin [146] worked on the concept of slot blowing on the 457
leading edges of the aerofoil of the VAWT blade. Satisfactory results obtained for studies 458
conducted on single slot-jet blowing and double slot-jet blowing led to patents filed by the owners 459
[147 – 151] . Claessens [201] used DMST to conducted studies on NACA 0018 airfoil and arrive 460
at a slightly modified shape that gives better aerodynamic and structural performance. Making the 461
end portion of the aerofoil flexible without affecting the overall shape of the aerofoil (fig. 5) has 462
been explored by earlier researchers with due benefits like improved starting characteristics. 463
Habtamu et al. [91] used DMST to verify the finding of CFD analysis which was part of a bigger 464
study to analyze airfoil modified to be flexible at 15° from the main blade axis of the turbine at the 465
trailing edge located about 70% of the blade chord length. 466
467
Fig. 5. Flexible trailing edge of the aerofoil 468
Steven [202] used DMST to study the performance of a new hybrid blade, blending Darrieus and 469
Savonius qualities. The new blade is found to perform better than traditional NACA 0012 airfoil. 470
Despite the known limitation of NACA symmetrical aerofoil’s of producing negative power 471
coefficient at lower tip speed ratios, the traditional researchers often shy away from using other 472
aerofoil’s owing to the symmetrical shape and reproducibility (using explicit formulas) of them. 473
The study by Mazharul et al. [114] quantitatively compares three different aerofoils (S8037, 474
SG6040 & S1210) against NACA0015 for smaller capacity VAWTs and concludes better 475
performance of the new aerofoils for lower tip speed ratios. 476
477
4.3 Out of the box ideas 478
In 1983, John et al. [135] introduced an optimization approach very different from the traditional 479
style wherein the upstream and downstream halves of the rotor through a differential treatment 480
linked the conceptualized model with fundamental mathematics. Through his studies, it was 481
proved that Betz limit for two uniformly loaded actuator disks in series was equal to 0.64 and for 482
a Darrieus straight bladed rotor was 0.61. The details of the development of a VAWT test bed was 483
described by Akshay et al. [161]. Based on the steps, an integration of prediction, design, and 484
testing of a 2 m × 2 m VAWT with slanted double blades was carried out. Ola Dwi et al. [165] 485
used single streamtube analysis along with experiments to study the effects of fins on Savonious 486
VAWTs. 487
488

The role of vehicles in wind energy can never be understated as their movement can induce strong 489
wind that comes handy for field testing applications [171] or to reach winds blowing at atmosphere 490
layers that are inaccessible by traditional wind turbines [172]. The paper by Narendra et al. [173] 491
describes the use of winds generated by the fast and perpetual motion of trains in powering the 492
rotation of VAWTs. The aerodynamic analysis is carried out by DMST. 493
494
5. Primary Application 495
496
The main reason for the introduction of streamtube theories is for the performance prediction of 497
VAWTs. It can be either predicting the performances of different VAWT shapes [177] with intent 498
on design or VAWTs with a particular constraint like micro VAWTs [179] or small scale VAWTs 499
with cambered blades [180], etc. The size of the application not being a limitation as SNL in its 500
early years leading to the research, used streamtube theories (even before the introduction of 501
DMST) for 34 meter Darrieus VAWTs [188, 189] . Apart from this very basic application, one of 502
most widely used application which even started with the very first introduction of the streamtube 503
theories by Templin [34] and continued all the way from there [36, 181 – 184] is the extension of 504
performance prediction to different solidities of VAWT. Researchers have defined solidity in two 505
distinct ways (given by equations 3 and 4). 506
507
Solidity =ே∗஼
ோ (3) 508
Or 509
Solidity =ே∗஼
ଶ∗ோ (4) 510
Where, N = Number of blades; C = Chord length and R = Radius of the Rotor. 511
512
The effect of solidity has been found to be significant on the performance of VAWT, and the 513
definition has been used to divide the VAWT, into low solidity VAWTs and high solidity VAWTs. 514
515
5.1 Comparison of new theories 516
517
A benefit of the streamtube theories explored in the past owing to its simplistic nature is to use it 518
as a comparison tool for new analysis methods. This comparison is not to arrive at any conclusions 519
on its face value as streamtube theories are not very accurate, but it helps in benchmarking the 520
newly developed theory. Bernard [185] used DMST to compare a new computational model 521
developed based on local circulation method generalized for curved blades combined with a wake 522
model. Allet [186] in a paper co-authored with Paraschivoiu used DMST for comparing a 523
numerical method based on the solution of the steady, incompressible, laminar Navier-Stokes 524
equations in cylindrical coordinates. Fernando et al. [187] developed a new method based on a 525
combination of free vortex model with a finite element analysis of flow and benchmarked it with 526
regards to DMST and Vortex methods as being more computationally intensive when compared 527
to the former but more accurate than the latter. 528
529

Dumitrescu et al. [204] used a DMST based improved code to examine a new method based on 530
lifting line theory and a free vortex wake model for predicting the performance of a three-531
dimensional VAWT. Radian [205] presented a simplified numerical technique for simulating 532
VAWT flow, based on the lifting line theory and a free vortex wake model, including dynamic 533
stall effects and tested it against the streamtube model. Anwelli [206] used DMST to validate a 534
new cascade theory based model developed for VAWTs. 535
536
5.2 Internal comparisons 537
538
Streamtube formulations find application for comparisons that are more intrinsic to them. In a 539
paper published in 1995, Brahimi et al. [29] compared findings using streamtube models, 3-D 540
viscous model, stochastic wind model and numerical simulation of the flow around the turbine 541
blades concerning developments of these methods up to that time. Robert et al. [207] used the 542
streamtube prediction for comparisons with wind tunnel experiments. Ibrahim et al. [208] used 543
multiple streamtube theory for comparison of straight blade and curved blade darrieus VAWTs. 544
Miau et al. [209] used DMST for a comparison of variable pitch control and fixed pitch control 545
VAWTs. A comparison of two dynamic stall models namely the Gormont model and a Leishman–546
Beddoes-type model was carried out by Eduard et al. [210] with the effects of flow curvature and 547
flow expansion included in the analysis. Asress et al. [240] compared the performances of CFD 548
and DMST for a darrieus VAWT with NACA0012 aerofoil. Franklyn et al. [292] on a study on 549
VAWT performance prediction using high and low fidelity analysis compared the results of CFD 550
with DMST. Gabriele et al. [293] used streamtube theories for a comparison of various 551
aerodynamic databases. 552
553
5.3 Optimization 554
555
Optimization studies have important application in the design of VAWTs. Even for a pitch 556
independent SB-VAWT there are at least six global parameters that can affect the performance of 557
a VAWT. They are: 558
1. Height of the rotor 559
2. Radius of the rotor 560
3. Number of Blades 561
4. Target angular rotation at rated wind speed 562
5. Aerofoil shape 563
6. Chord length of the blade 564
565
Apart from these, some other local parameters can affect the performance of a VAWT. For a non-566
straight bladed VAWT, at least one extra parameter (for defining the non-straight shape) becomes 567
part of the optimization exercise. The complexity is maximum when all the geometric variables 568
vary with the height of the rotor. Fig. 6. shows one such model that was developed by the authors 569
as part of a testing program planned at IISc Bangalore. 570
571

572
Fig. 6. Complex shaped VAWT 573
574
Streamtube theories are the most convenient method for optimization exercises. Re-running the 575
analysis after changing the parameters are the quickest with regards to computational effort and 576
time. On the other hand, in comparison with other methods like CFD analysis, the extra effort in 577
re-runs include changing the parameter for the new model, modifying the mesh around the 578
modified region, making the model error-free with the particular configuration along with the 579
significant computational time that follows for the analysis. 580
Numerous optimization studies have been carried out using streamtube theories. WuFaMing [211] 581
developed an optimization model for Darrieus SB-VAWT based on analysis conducted using 582
DMST. Jens et al. [212] investigated the effect of camber and pitching angle of wing profile on 583
optimization of power output. Shuangqing et al. [213] carried out an optimization study by 584
considering the radius of the rotor, number of blades, chord length, and the blade height as 585
variables. Diego et al. [236] carried out studies on the optimal angle of the blades by finding out 586
the angular position that generates the most torque possible for the turbine rotation. 587
5.4 Effect of certain parameters 588
A lot of studies used streamtube theories to single out the effect of individual parameters on the 589
performance of the VAWT. Elmabrok et al. [233] used DMST to explore the effect of various 590
geometric parameters on the self-starting characteristics of VAWT. Ibrahim et al. [234] studied 591
the effect of the number of blades, chord to radius ratio, solidity, height to radius ratio and 592
Reynolds number on the performance of VAWT. Dhruv [235] simulated the effects of winds 593
speed, blade pitch and Tip Speed Ratio (TSR) on blade loads. DMST modified with dynamic stall 594
model (Boeing-Vertol model & ONERA model Risφ model) used by Huang [237] for an 595
investigation into dynamic stall effects. Arti et al. [238] studied the effect of blade profile, number 596

of blades, Reynolds number and aspect ratio on the performance of VAWT using multiple 597
streamtube theory. Raluca et al. [239] investigated the effect of aspect ratio and aerofoil shape on 598
the performance of darrieus VAWTs. 599
600
5.5 Pitch based studies 601
For a phase during the revival of VAWT concept, pitch based studies have taken the spotlight. 602
Researchers have focused on experimentation and numerical modeling of variable pitch 603
mechanisms and other pitch related concepts mostly limited to medium or small sized VAWTs. In 604
most of such studies, streamtube formulations have been used with geometric modification of 605
existing formulations to accommodate the pitch variation. Fig. 7 shows the mechanism of a simple 606
variable pitch VAWT. 607
608
609
Fig. 7. Mechanism of variable pitch VAWT 610
611
In a paper published in 1992, Lazauskas [241] used an extended DMST model that included flow 612
curvature effects and streamtube expansion, and which incorporated a Boeing-Vertol dynamic stall 613
model to compare three variable pitch mechanisms for VAWTs. Lazauskas with his works on 614
pitching mechanisms inspired Brian [242] who worked on the analysis of self-acting variable pitch 615
VAWTs. Wolfgang [16] Used DMST in the design of a wind turbine for residential use with the 616
study on the effect of pitching the blades over a range of wind speeds. Conaill et al. [20] proposed 617
an analytical model based on DMST for calculating the rotor performance and aerodynamic blade 618
forces for SB-VAWTs with variable pitch. 619
620
621
622
5.6 Small scale VAWTs and location-based studies 623

Although HAWTs and VAWTs are competitors with each other, they have adopted contrasting 624
styles in their development. While much of the research activities of HAWTs recently have been 625
focused on building larger sized rotor with stronger but lightweight composite blades; VAWTs, 626
on the other hand, have been explored for its adaptability for small scale or stand alone 627
applications. The VAWTs helped by their low environmental impact are better adapted to be 628
installed nearby the urban and residential areas because they have low noise level and lower start-629
up speed. These are also appropriate for installation in areas with high winds due to their omni-630
directional nature [243]. The small scale and stand-alone applications often bring to design the 631
local wind and climatic patterns of the area under consideration. 632
633
Samaraweera et al. [244] developed a theoretical model for the design and performance simulation 634
of Darrieus-type vertical axis stand-alone wind turbines for small-scale energy applications. Javier 635
[245] used DMST analysis to design a small VAWT rotor with solid wood as a construction 636
material for operation under low TSR. Ji Xiao [246] carried out design and analysis of small scale 637
fixed-pitch SB-VAWTs. McGowan et al. [179] developed a model to guide the design and predict 638
the performance of micro VAWTs using multiple streamtube theory. 639
The influence of site specific characteristics is owing to the location based design that inevitably 640
creeps into the design. Table 3 shows some such studies that used streamtube theories in their 641
computations. 642
643
Country /
Continent Region Brief description Ref.
Argentina Patagonia Used streamtube model to estimate Darrieus VAWT
performance for applications in the North-western
Patagonia region of Argentina [247]
Antarctica Amundsen-Scott
South Pole Station Used conformal mapping and DMST model on
designing an SB-VAWT for a real project planned in
Antarctica [13]
Trinidad
& Tobago (whole of) DMST used for analysis of an economical darrieus SB-
VAWT for domestic applications [248]
Iran Khorasan Design and optimize the site-specific H-rotor type
VAWT using BE -M and a DMST model [249]
Vietnam (whole of) Propose design parameters for the design of a 1kW
straight bladed vertical axis wind turbine, to serve
energy needs for families in Vietnam [92]
UAE Masdar City Performance prediction small scale fixed pitch VAWT
using NACA0015 and NACA0018 airfoils [178]
Table. 3: Location specific studies 644
645
646
647
6. Advanced Application 648

649
Apart from the primary applications discussed in the previous section, there some applications that 650
do not use the results of streamtube theories as it is but use the results as a stepping stone to 651
compute other variables. A discussion of some of those applications referred here as “advance 652
application” is provided in this section. 653
654
6.1 Structural Calculations 655
656
The natural progression of loads calculated through streamtube analysis is to use it for structural 657
calculations. In 1976, before the introduction of DMST and even before the proper development 658
of multiple streamtube theories, Robert et al. [250] observed that the aerodynamic formulations 659
based on multiple stream tube approach requiring iteration techniques look impractical for 660
coupling with the structural behavior. The development of DMST has only compounded the 661
problem requiring additional iterations for the downwind half of the rotor. However, the 662
improvement of computational resources coupled with a more accurate refinement of streamtube 663
theories has led to the natural progression of streamtube analysis results for use in structural 664
calculations. The SNL experimentations on 34-meter VAWT with a focus on the structural aspects 665
of Darrieus VAWTs used the predictions of streamtube theories for calculations [251, 252] . 666
Structural analysis based codes like FFEVD [253] and TRES4 [254] used the imported values of 667
aerodynamic loads. Lobitz [255] in his dynamic analysis program, VAWTDYN used single 668
streamtube model for aerodynamic loads. 669
6.2 Tidal turbines 670
A natural beneficiary of the development of streamtube theories has been tidal or hydro turbines. 671
As wind and water come under the common umbrella of fluids, the theory that governs the former 672
is extensible to the latter with expected differences in the finer aspects. The first applications of 673
streamtube theories to tidal turbine were present as early as 1980’s with works of Hilton [338] 674
comparing the findings with experimental results and extending the study to different solidities. 675
Gareth [256] in his work coupled streamtube models with CFD analysis to carry out the 676
hydrodynamic analysis of a vertical axis tidal current turbine. Winchester et al. [257] used DMST 677
with Gormont-Berg adaptation of dynamic stall for comparing "torque ripple" and variable blade 678
forces of Darrieus and Gorlov-type turbines for tidal stream energy conversion. Hongbo et al. [258] 679
used single streamtube modeling to study the effect of blade number, blade chord, rotor radius and 680
blade density on vertical axis tidal turbine performance. 681
Qing-Jie et al. [259] used DMST to develop a mathematic optimization model to enhance the 682
power coefficient of vertical-axis turbine for tidal current conversion by adjusting the blades 683
deflection angle. The streamtube model has been used to study losses due to struts, the effects of 684
a velocity profile and to design a turbine for deployment in a river by Anders [260]. Paraschivoiu 685
et al. [261] compared the hydrodynamic performances and structural responses of different vertical 686
axis hydrokinetic turbines. Lazauskas used DMST based program VAWTEX-B for modeling 687
passive variable pitch cross flow hydrokinetic turbines [19]. 688
The publications based on usage of streamtube theories for tidal turbines rose greatly in the past 689
two years. Marsh et al. [262] used DMST for simulating the performance of a vertical axis tidal 690

turbine. Ashuri et al. [263] used DMST to develop a hydrodynamic model to predict the 691
performance and the loads on the turbine blades. A coupling method between the ONERA-EDLIN 692
model and a streamtube model has been implemented successfully to model the performance of a 693
Darrieus-like water turbine with active pitch variation by Paillard et al. [120]. Daniel et al. [264] 694
used DMST formulations to do the initial design of an H-Type darrieus tidal turbine. Norbert et 695
al. [265] investigated the dynamic response of single and multiple rotor Darrieus-type vertical axis 696
water turbines using DMST to determine the best configuration. Prabhu et al. [266] carried out 697
performance prediction of H-Type darrieus turbine by single streamtube model for tidal 698
applications. Anders et al. [267] performed simulations of a vertical axis turbine in a channel. Eren 699
[268] compared the findings of DMST with 2-D CFD analysis on a study aimed at designing a 700
Darrieus type vertical axis turbine for tidal applications. 701
6.3 Multi-disciplinary applications 702
703
Certain interesting studies and applications that span across disciplines have used streamtube 704
theories in their calculation of aerodynamics of the rotor. Martino et al. [269] compared different 705
VAWT configurations obtained by differing the methodology of fastening of the blade to its 706
spokes. Bhatta et al. [270] used DMST to develop a dynamical systems model and control 707
algorithm for a small VAWT for use in regions without very favorable wind conditions. Moble et 708
al. [271] used DMST for analysis of Cyclorotor and Cyclocopter used in flying. These devices are 709
like VAWTs placed horizontally. Conaill et al. [272] proposed a new approach for smoothing the 710
power fluctuations from aggregated VAWTs through internal adjustments between VAWTs in the 711
group. The analysis of VAWTs on its suitability for roof-top installation with considerations of 712
the skewed flow conditions was taken up by Francesco et al. [17]. The analysis was carried out 713
about a European city. 714
Xiaomin et al. [273] used a wake model based on single streamtube theory for wind farm layout 715
optimization using the genetic algorithm. Altab et al. [274] used artificial neural networks to 716
develop a fuzzy expert system aimed at achieving a more realistic evaluation of wind power 717
extraction. Tetsuya et al. [275] developed a performance monitoring method for stand-alone 718
VAWTs which does not require the use of a wind speed sensor. Alessandro et al. [276] developed 719
design guidelines for H-Darrieus wind turbines for optimization of the annual energy yield. Leyre 720
[277] developed a program that is capable of calculating the vibrations of the wind turbines tower 721
more accurately. Vimal et al. [285] and Miloš [286] through their publications have discussed the 722
details and technicalities supported by calculations on the installation of VAWTs in Mars. 723
724
6.4 Offshore VAWTs 725
726
Certain advantages of VAWTs over HAWTs have made them a real competitor [72] in offshore 727
conditions. The analysis of offshore VAWTs adds a level of complexity when compared to 728
VAWTs installed on shore as the effect of wave forces comes into consideration. With an emphasis 729
on start-up and shut-down schemes, Harald et al. [278] analyzed the Deepwind floating VAWT 730
concept. A DMST based model that captures dynamic stall effects has been used to calculate the 731
Fourier coefficients. Wang et al. [279] carried out dynamic analysis of a floating VAWT under 732
emergency shutdown using a hydrodynamic brake. A new grant support scheme started by certain 733
European countries called H2Ocean is leading to valuable contributions through a series of 734

publications by Michael [280, 281] and Michael et al. [27, 282 – 284] on floating VAWT concept. 735
The analysis of the aerodynamic part is carried out using DMST. 736
737
7. Comparative State-Of-The-Art 738
739
Numerous related state-of-the-art papers published in the past decade has mentioned the 740
streamtube theories as a significant development. Ahmet [287] in his article on “Progress and 741
recent trends in wind energy” identifies momentum models alongside vortex and finite difference 742
methods as the three approaches that can be used to solve the wind turbine flow physics. Mazharul 743
et al. [288] in his review paper based on simplified models for SB-VAWT identifies vortex model, 744
cascade model & momentum models as the three major approaches for analysis with their accuracy 745
levels in the mentioned order and computational efforts in the reverse order. Aldo [289] in his 746
multi-faceted book chapter on wind energy discusses the single streamtube, and multiple 747
streamtube approaches with a focus on experiments and comparisons of SNL. 748
NRC of Canada was an integral part of SNL activities on Darrieus VAWTs and streamtube theory 749
developments although the contributions of NRC are slightly underrated owing to the limited 750
amount of published literature. Benmeddour et al. [290] provide an overview of research activities 751
and facilities at NRC with a mention of the usefulness of DMST predictions and improvements in 752
its capabilities after incorporating the effects of dynamic stall. Xin et al. [296] in a paper on 753
different analysis approaches for darrieus VAWTs have provided a detailed account of streamtube 754
theories, their comparison with other methods and some insight into recent research trends. 755
756
8. Future of Streamtube Theories 757
758
The section provides a window into the future of the streamtube theories based on a global 759
overview of the developments till now. The streamtube theories are certainly on the path of more 760
refinements as evident from more accurate models proposed and with the use of new generation 761
tools like genetic algorithm along with its formulations. A discussion on the two sides of 762
streamtube theory usages is provided henceforth (section 8.1 and section 8.2). 763
764
8.1 Limitation of streamtube theories 765
766
Four decades have passed since the introduction of classical streamtube theories. The theory has 767
undergone quite a lot of refinement over the years. Despite these, the theory still lacks perfection 768
in areas of modeling high tip speed ratio, high solidity, blade wake interaction, etc. These 769
deficiencies have led some researchers to opt for more accurate methods of analysis. Table 4 gives 770
a list of research works that had the option of using streamtube theories in their works but choose 771
otherwise due to particular reasons. The year of the publication has also been included to provide 772
a perspective on the level of streamtube theory development then. 773
774

Reason specified Year Ref.
Unable to model time-dependent analysis and inability to model shed vorticity
and its interaction with the blades 1976 [297]
Failure to model turbulent wake state 1984 [298]
Streamtube theories are not applicable to the unstable regimes 1986 [299]
Method does not provide detailed aerodynamic information 2004 [300]
Recent improvements in computational power have enabled use of more
accurate (more computationally intensive) methods 2004 [301]
Accurate and computationally intensive CFD is affordable 2006,
2008 [302,
303]
Dynamic stall related inaccuracies 2007 [304]
Inability to accurately capture 3 -D effects 2007 [305]
Streamtube theories exhibit difficulties in predicting the instantaneous forces
on the blades and the details of the flow field 2007 [306]
Inability to accurately model the complex flow physics related to shedding
vortices in high solidity VAW Ts 2008 [307]
The computational cost of the model used is of the same order as the
streamtube models 2009 [308]
Streamtube theories are unable to account accurately for flow curvature
influence and blade –wake interaction 2009 [309]
Streamtube models unsuitable for the calculation of unsteady blade loads as a
result of their quasi -steady formulation 2009 [310]
Over-predicts power for a high-solidity turbine and the approach appears to be
invalid for large tip speed ratios 2009 [311]
DMST limited in c ases of high solidity ratio, dynamic stall & flow curvature 2010 [312]
Streamtube theories tend to break down for high tip speed ratios and high
solidities where viscous effects become dominant 2010 [313]
Increased availability of high-performance computing has allowed the use of
more accurate methods 2011 [314,
315]
DMST was unusable as the rotor has high solidity and low TSR and the results
in iterative process did not allow converged solution 2011 [316]
DMST assumptions limit its usefulness for high solidity turbines 2011 [317]
Lacking technology innovation to predict the performance highly complex
VAWT aerodynamics 2012 [318]
Not capable of predicting the flow physics beyond stall 2012 [319]
Streamtube theories are not accurate enough to analyze detailed design 2012 [320]
Their quasi-steady state foundations are not suitable for calculations of the
complex flow patterns involving blade-wake interaction and dynamic stall
effects that are prominent in high solidity turbines that operate at low tip speed
ratios 2012 [321]
They are stationary models and take into account the time-averaged cumulative
effects of the rotating blades. The models break down for higher tip speed
ratios and also for high solidity ratios. 2012 [322]
Momentum models cannot consider the wake effect rigorously 2013 [323]

These models are one-dimensional and are unsuitable for curved bladed
turbines 2013,
2014 [324,
329]
Over-estimation of performance at low speeds 2013 [325]
Inability to investigate the complex unsteady flow 2014 [326]
High solidity of savonius rotor limit the application of streamtube theories 2014 [327]
Streamtube theories are unable to capture the near -blade flow physics 2014 [328]
DMST model is not suitable for high tip speed ratios and high solidity VAWT 2014 [330]
One dimensional simplified equation that does not provide information on the
wakes and they use semi-empirical equations to predict effects like tip vortex
and dynamic stall. They also need accurate experimental data for aerodynamic
coefficients of the airfoils 2014 [52]
Drawback of streamtube models is the requirement of aerodynamic
characteristic of airfoil and empirical formulas of dynamic stall 2015 [53]
Streamtube theories cannot solve for boundary layer velocity profiles or
turbulent inflow parameters 2015 [331]
Accuracy of streamtube theories is only a result of the cancelation of errors 2015 [332]
Limited to low TSRs and small solidities 2015 [333]
Table. 4: Studies that eluded streamtube usage for computation (with reasons) 775
776
777
8.2 Use of earlier streamtube models 778
779
Based on the discussion in section 8.1 and Table 4, it is logical to conclude that the streamtube 780
theories have a lot to achieve concerning user acceptability. However, despite the known improved 781
accuracy of DMST over earlier streamtube theories, some researchers insist on using the previous 782
versions of streamtube theories. Table 5 provides an incomplete list of many such cases 783
encountered. As with Table 4, the year has been mentioned to offer a perspective on the level of 784
streamtube theory developments at that point of time. 785
786
Theory
used Reason specified (if any) Year – [Ref.]
Before
DMST S –
1976 – [336], 1978 – [337], 1980 –
[255], 1980 – [48], 1981 – [50]
After
DMST S – 1992 – [269], 2000 – [142], 2001
– [240], 2012 – [273], 2013 –
[165], 2013 – [266], 2013 –
[135], 2014 – [216], 2015 – [176]
S The accuracy levels of single
streamtube method was sufficient
as the goal was only to find
performance improvements
resulting from control 2010 – [144]
S Used Single streamtube model as
the study was only to determine 2010 – [258]

the effect of various parameters
on performance
SD – 2012 – [246]
SD To reduce program running time 2013 – [120]
SG – 2012 – [236]
S & M – 2011 – [145], 2012 – [146]
M – 1987 – [339], 2007 – [100], 2008 –
[101], 2009 – [199], 2010 – [205],
2010 – [244], 2011 – [234], 2012
– [161], 2012 – [179], 2013 –
[24], 2013 – [203], 2014 – [213],
2014 – [128]
M DMST is more complicated to
program and difficult in
implementation compared to
earlier models 2011 – [212]
M Adopted Multiple streamtube
model instead of DMST as the
study was for overall comparison
of two types of rotors 2012 – [208]
M The application was for low
solidity, high rotational speed
VAWT, and the dynamic stall
effect was minimal where
multiple streamtube theory itself
provided sufficient accuracy 2015 – [129]
Table. 5: Usage of earlier streamtube theories (S – Single, M – Multiple, SG – Single W/Glauert, 787
SD – Single with double disk) 788
789
As evident from Table 5, not many users have provided reasons for non-usage of more accurate 790
versions of the streamtube theories. However, based on the reasons given, it is logical to believe 791
that the primary purposes of using streamtube theory justified the lower accuracy achieved with, 792
the earlier versions of the streamtube theories. These contrasting but interesting observations 793
(based on Table 4 & Table 5) of streamtube theories testifies to its simplistic nature that has 794
reached a point of saturation. Any amount of refinement of the streamtube theories for more 795
accuracy would only mean a more complicated streamtube model which certain research works 796
(like those mentioned through Table 5) may not be interested in applying. 797

The above point is better visualized in the following way. Let us imagine that at a future date (say 798
the year 2030) that the streamtube models became so refined that it is now able to provide accurate 799
predictions for high TSRs, high solidities & wake based modeling (which are deficiencies with the 800
current models). Such a refinement would mean a more complicated model that the basic attraction 801
of streamtube theories of being simple and computationally less intensive would not be valid 802
anymore. Fig. 7 depicts this hypothetical balance between accuracy and simplicity. 803
804
Fig. 8 Hypothetical balance representing simplicity of the model to its accuracy 805
Hence, even in 2030 with the refinements as mentioned above, the researchers similar to those 806
referred to in Table 5 would continue to use the streamtube theories as it was in its earlier form 807
without much focus on the later developments. Nevertheless, the academic value of the 808
refinements is never looked down but the primary justification for using streamtube theories as 809
being simple and easily programmable would go away. An additional point that needs mention is 810
that the added complexity (as part of a refined model) would mean that researchers working in this 811
field would no longer be able to write own codes as mentioned in Table 1 but there would big 812
software’s that would carry out streamtube computations. As with CFD, RANS and other 813
computationally intensive methods which require big software’s, streamtube theories also would 814
follow the path. An issue related to it is that the computational steps done by the software would 815
remain largely as a black box for the primary user who can get the result just with the click of a 816
mouse without knowing what the software does. The over dependence on computing resources 817
with limited knowledge of the actual steps involved is a great calamity of our times with the 818
revolution of computational resources worldwide [341]. 819
820
Conclusion 821
Streamtube theories have come a long way since its first introduction in 1974. The simplicity of 822
the approach despite its known inaccuracies has made it a quick analysis tool for engineers working 823
on VAWTs. This paper discusses the past, present and future of streamtube theories concerning 824
the theoretical developments, applications and usage trends. The streamtube theories have 825
positively affected a lot of areas of VAWT design. The usage pattern is indicative of the fact that 826
the developments of streamtube theories as a simplistic tool for analysis have reached the point of 827

saturation. Future refinements of the model would be beneficial for its academic value and in 828
reducing the inaccuracies but at the cost of losing its “simple method” tag. 829
830
Acknowledgement 831
832
Writing this review paper would not have been possible without the precise documentation of 833
reports and workshops held by Sandia National Laboratory (SNL) starting from the 1970’s. 834
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