**3. Double, multiple streamtube model (DMS), CARDAAV code**

In the Double, Multiple Streamtube models (DMS) developed initially been by Paraschivoiu [11, 29], the variation in the upwind and downwind induced velocities as a function of the azimuthal angle has been included. In this case, the wind turbine blade is divided into several elements assuming no interaction between the components. This method's main principle is to determine the axial and angular induction factors using an iteration method. Then, the forces and power generated are defined in a similar manner to the VAWT. **Figure 1** shows the double streamtube model principle where the machine is represented by a pair of actuator disks in tandem in the upwind and downwind zone, CARDAAV Code. The induced velocity decreases in the axial direction so that the downwind induced velocity is smaller than the upwind zone. With *V*∞*i* representing the local ambient wind velocity, *Ve* the equilibriuminduced velocity as shown in **Figure 1**, we can write the induced velocities as a function of the induced factor in the upwind zone named *a* and downwind zone named *a*0 *:*

$$V = a \; V\_{\approx i} \tag{1}$$

$$V\_{\epsilon} = (2\mathfrak{a} - \mathfrak{1})V\_{\lnot \mathfrak{i}} \tag{2}$$

$$V' = a'V\_{\varepsilon} = a'(2a - 1)V\_{\infty i} \tag{3}$$

$$W^{\prime\prime} = (2a^{\prime} - \mathbf{1})(2a - \mathbf{1}) \text{ V}\_{\approx i} \tag{4}$$

**Figure 1.** *Principle of the double multiple streamtube model.*

The atmospheric wind shear in Eq. (5) is based on the Frost *et al.* model [30] where *ZEQ* represents the height at the equator, *V*∞*i* is the local ambient wind velocity in the vertical direction, *V*∞ is the ambient wind velocity at the equator, and *α*∞*i*is the exponent of the power-law, which in our simulation is taken to be 1*=*7.

$$\frac{V\_{\infty i}}{V\_{\infty}} = \left(\frac{Z\_{\infty i}}{Z\_{EQ}}\right)^{a\_{\infty i}}\tag{5}$$

The relative velocity and the local angle of attack in the upstream zone where the azimuth angle varies between �*π=*2≤ *θ* ≤*π=*2, are given by:

$$\mathcal{W}^2 = V^2 \left[ \left( X - \sin \theta \right)^2 + \cos^2 \theta \cos^2 \delta \right] \tag{6}$$

$$a = \arcsin\left[\frac{\cos\theta\cos\delta}{\sqrt{\left(X - \sin\theta\right)^2 + \cos^2\theta\cos^2\delta}}\right] \tag{7}$$

where *X* ¼ *ωr*is the tip-speed ratio, and *ω* is the turbine rotational speed. For the downwind zone where the azimuth angle varies between *π=*2≤*θ* ≤3*π=*2 similar equations can be derived using *W*0 and *α*0 . The nondimensional normal and tangential forces as a function of the azimuth angle *θ* are given by

$$F\_N(\theta) = \frac{c}{S} \int\_{Z\_R}^{Z\_R + 2\mathcal{H}} \left(\frac{W}{V\_{\infty}}\right)^2 \mathcal{C}\_N dZ \tag{8}$$

$$F\_T(\theta) = \frac{c}{S} \int\_{Z\_R}^{Z\_R + 2H} \left(\frac{W}{V\_{\infty}}\right)^2 \frac{C\_T}{\cos \delta} dZ \tag{9}$$

Using the same modeling above for the upwind region, the downwind area can also be calculated with the azimuth angle between *π=*2 <*θ* < 3*π=*2*:* The normal and tangential force coefficients of the blade section are given by

$$\mathbf{C}\_{N} = \mathbf{C}\_{L}\cos\alpha + \mathbf{C}\_{D}\sin\alpha \tag{10}$$

$$\mathbf{C}\_{T} = \mathbf{C}\_{L} \sin a - \mathbf{C}\_{D} \cos a \tag{11}$$

where the lift and drag coefficients CL and CD are computed by interpolating the available test data using both the local Reynolds number Re ¼ Wc μ∞ � � and the local angle of attack. These coefficients are used up to an angle close to the static stall angle, from which point a dynamic-stall model is considered to estimate the dynamic lift and drag coefficients. The equations for the interference factor *a*ð Þ*θ* are given by [11].

$$K[\mathbf{1} - a(\theta)] \cos \theta = a(\theta) f(\theta) \tag{12}$$

$$f(\theta) = \left(\frac{W}{V}\right)^2 \left[\mathbf{C}\_N \cos \theta + \mathbf{C}\_T \left(\frac{\sin \theta}{\cos \delta}\right)\right] \tag{13}$$

where K ¼ 8πr Nc and N is the number of blades. The upwind half-cycle of the rotor is divided into several angular tubes Δ*θ*, assuming a constant induced velocity for each of these tubes, **Figure 2**. The interference factor *a*ð Þ*θ* can be written as

$$a(\theta) = \frac{K\mathcal{K}\_0}{K\mathcal{K}\_0 + \int\_{\theta - \frac{\theta^\theta}{2}}^{\theta + \frac{\theta^\theta}{2}} f(\theta)d\theta} \tag{14}$$

*Aerodynamic Analysis and Performance Prediction of VAWT and HAWT Using CARDAAV… DOI: http://dx.doi.org/10.5772/intechopen.96343*

**Figure 2.** *VAWT model: (a) integration points, (b) DMS model.*

where K0 ¼ sin *θ* þ Δ*θ* 2 � � � sin ð Þ *θ* � Δ*θ=*2 and *a*ð Þ*θ* is computed numerically. A similar technique is then used for the downwind zone to determine the interference factor *a*0 ð Þ*θ* . The torque produced by the blade element as a function of the azimuth angle is calculated based on the lift and drag contributions *CQL* and *CQD*

$$\mathbf{C}\_{\mathrm{Q}\_{L}} = \frac{\mathrm{Nc}}{2\pi \mathrm{SR}} \int\_{-\pi/2}^{3\pi/2} \int\_{Z\_{R}}^{Z\_{R} + 2H} \mathbf{C}\_{L} \mathrm{s} \mathrm{s} \mathrm{a} \left(\frac{W}{V\_{\infty}}\right)^{2} \times \left(\frac{r}{\cos \delta}\right) d\mathbf{Z} d\theta \tag{15}$$

$$\mathbf{C}\_{\rm Q\_D} = \frac{\rm Nc}{2\pi \rm SR} \int\_{-\pi/2}^{3\pi/2} \int\_{Z\_R}^{Z\_R + 2H} \mathbf{C}\_D cos \alpha \left(\frac{W}{V\_{\infty}}\right)^2 \times \left(\frac{r}{cos \delta}\right) d\mathbf{Z} d\theta \tag{16}$$

Finally, the power generated due to the lift and the losses due to the drag is given by

$$P\_L = \frac{1}{2} \rho\_{\text{ss}} V\_{\text{ss}}^3 \text{S}(\text{C}\_Q)\_L \frac{\text{o}R}{V\_{\text{ss}}} \text{ and } P\_D = \frac{1}{2} \rho\_{\text{ss}} V\_{\text{ss}}^3 \text{S}(\text{C}\_Q)\_D \frac{\text{o}R}{V\_{\text{ss}}} \tag{17}$$

The impact of atmospheric wind turbulence on a wind turbine's aerodynamic loads can be included in the DMS model using a stochastic atmospheric wind. The induced velocities necessary for predicting the forces were computed for each Streamtube in both the upwind and downwind zones of the rotor, including the longitudinal and lateral fluctuation velocities resulting from the fluctuating atmospheric wind. A wind time series in the rotor's upwind zone is created to produce the turbulent wind velocity. Using a time delay in the time series based on a linear variation, the turbulent wind speed in the downwind zone is generated [11]. The total velocity of the fluctuating atmospheric wind is a superposition of a mean part and a stochastic fluctuating part. The values of the fluctuations velocities are performed by using the Fast Fourier Transform. The time series are assumed to propagate downstream of the rotor with the speed of the airflow disturbed by the presence of the wind turbine. The simulation uses Double-Multiple Streamtube model (DMS) with up to 1512 stream tubes for the whole Darrieus rotor (21 vertical stream tubes and 72 lateral stream tubes at every five degrees [11]. In the presence of atmospheric turbulence, the relative velocity and the local angle of attack are given by [18]:

$$\mathbf{W}^2 = \left[ (\mathbf{V} + \mathbf{u}\_\mathbf{f}) \sin \theta + \mathbf{v}\_\mathbf{f} \cos \theta - \alpha \mathbf{r} \right]^2 + \left[ \mathbf{v}\_\mathbf{f} \sin \theta - (\mathbf{V} + \mathbf{u}\_\mathbf{f}) \cos \theta \right]^2 \cos^2 \theta \tag{18}$$

$$\mathbf{a} = \arcsin\left[\frac{\mathbf{v}\_{\text{f}}\sin\theta - (\mathbf{V} + \mathbf{u}\_{\text{f}})\cos\theta}{\mathbf{W}}\right] \cos\delta\tag{19}$$

where *V* is the upwind velocity and *u f* and *v f* the fluctuation velocity components. The overall model developed "CARDAAS" performs the computation of steady-state, CARDAAV as well as the stochastic response of aerodynamic loads when turbulence is included [11, 18, 22].


**Conflict of interest**

The preparation of this chapter was not funded by Gulfstream, and it was done by the author using his own time and resources; thus, it does not represent the Gulfstream's view on the results presented in this chapter.


**2.4 Syntheses of ylidenebutenolide modified derivatives and the stereochemical and spectral characteristics of the synthesized derivatives**

Finally, the synthesis of ylidenebutenolide modified peridinin derivatives is described. The acetylene ester derivative was synthesized by the same protocol. Namely, the coupling between C17-allenic segment **10** and C20-acetylene methyl ester segment **16** by using the modified Julia olefination, which was followed by the isomerization gave all-*trans* **8** (Fig. 8 (A)) (Kajikawa et al., 2010).

On the other hand, there were some difficulities in the synthesis of the olefin ester derivative (Fig. 8). We obtained the only 9'E-olefin ester segment **17** by the similar synthetic process, which was not the desired 9'Z half-segment resulting from the contribution of the carbonyl group of the methyl ester. We then tried to connect the segments **10** and **17** by the modified Julia olefination and to obtain all-*trans* **9-3** by the isomerization. The anion derived from **10** was stirred with a mixture of stereoisomers of **17** under the same conditions used for the coupling of the previous peridinin derivatives. The reaction was completed within 5 min in the dark to produce the coupling products as a mixture of the stereoisomers in 46% amount, whose HPLC is shown in Fig. 8 (B). The major peak (peak 1) was estimated to be 45% of the mixture by HPLC analysis (other isomers were 16%, 14%, 5%, 5%, and others). Isomerization to the desired all-*trans* **9-3** was attempted under the same conditions previously used. After 5 days, the initially generated major peak (peak 1) changed to another peak (peak 2; 44% based on HPLC analysis) in an equilibrium state. We then isolated both compounds and elucidated their structures by NMR (400 and 750 MHz), and clarified that peak 1 was (13Z, 9'E)-isomer **9-1** and peak 2 was (13E, 9'E)-isomer **9-2**. Unfortunately, we could not obtain the desired all-*trans* (13E, 9'Z)- isomer **9-3**.

We investigated the stability of the synthesized ring opened derivatives **8** and **9**, and found the isolated all-*trans* acetylene ester derivative **8-1** was more labile than **8-2** (13Z-isomer). For instance, the isolated all-*trans* derivative **8-1** (13E-isomer) isomerized to the dihydrofuran derivative **8'** by a trace amount of hydrogen chloride in CDCl3, but the corresponding isomerization of **8-2** (13Z-isomer) was not observed (Fig. 8). In addition, the all-*trans* derivative **8-1** rapidly isomerized to give a mixture of Z-isomers upon illumination. This might occur due to the contribution of the carbonyl group of the methyl ester similar to the case of the 9'E-olefin ester derivative **9-2**.

In the PCP complex, peridinin exhibits an exceptionally high efficiency of energy transfer to Chl a. In order to make clear the effect of the ylidenebutenolide, we needed to measure the energy transfer efficiencies in peridinin derivatives. Futhermore, it was tried to construct the corresponding PCP derivatives using the synthesized peridinin derivatives **8** and **9** to compare with the energy transfer efficiencies of peridinin (private information from Dr. H. A. Frank). First, it was attempted to reconstitute the PCP apoprotein using the 9'E-olefin ester derivative **9-2** under the same conditions that were successful for peridinin (Ilagan et al., 2006), but the reconstitution was not observed. It was also tried to reconstitute the PCP apoprotein using the 13Z-isomer **8-2**, but it did not bind the protein either. The reason might be that these compounds were bent into a *cis* configuration, and hence they might not fit properly into the protein binding site. These results apparently showed that the ylidenbutenolide of peridinin at least contributes to the stereochemical stability of the

An Approach Based on Synthetic Organic Chemistry Toward Elucidation

AcO OH •

Allene function

AcO OH •

AcO OH •

AcO OH •

AcO

AcO

AcO

**peridinin**

O

**2**: Acetylene Derivative

438.0 nm

450.0 nm

459.0 nm

**3**: Olefin Derivative

**4**: Diolefin Derivative

O

of Highly Efficient Energy Transfer Ability of Peridinin in Photosynthesis 145

C37-Peridinin (**1**)

454.0 nm

O O

**5**: C33-Peridinin Derivative

**6**: C35-Peridinin Derivative

**7**: C39-Peridinin Derivative

**3. Relationships between the unique structure and the special exited state of**

From studies on peridinin and other carotenoids, it has been known that there are at least two important low-lying excited singlet states, denoted S1 and S2, which are related to the highly efficient energy transfer from peridinin to chlorophyll a (Fig. 10(A)). To elucidate the mechanism of this efficient energy transfer, it is important that we make clear the characteristics of these excited states and the energy transfer pathways such as those from S2 to QX and/or from S1 to QY.  The conjugated double bonds of most carotenoids are symmetry and these double bonds can be regarded as polyenes described in terms of the idealized C2h point group in the spectroscopic fields (Hudson et al., 1973). The lowest excited singlet (S1) state is assigned to the 21Ag- state, and the second lowest singlet (S2) state is assigned to the 11Bu+ state. The excitation to S1 from the ground state is symmetry forbidden and is not directly accessible by one-photon processes in contrast to the allowed absorption to S2 state (Polivka et al., 2004). On the other hand, the conjugated double bond of peridinin and other carbonylcontaining carotenoids are asymmetric due to the presence of the conjugated carbonyl group, and these oxygenated carotenoids display a pronounced solvent dependence of its lowest excited singlet state lifetime (S1 lifetime). Namely, it has been proposed that the findings are consistent with the presence of an intramolecular charge transfer (ICT) state, which is uniquely formed in carotenoids containing the carbonyl group in conjugation with the -electron system of double bonds (Frank et al., 2000; Zigmantas et al., 2004). It has also been argued that changes in the position of the ICT state related to the S1 state rationalize the dependence on solvent polarity concerning S1 lifetime. In the case of peridinin, the relationship of these energy levels is well discussed based on the detailed experimental works. The ICT in the excited state manifold of peridinin is shown to be higher in energy than the S1 state in nonpolar solvents and shifts below S1 with increasing solvent polarity

Fig. 9.

The maximum absorption wavelengths (max) in the electronic spectra of peridinin (**1**) and the synthesized derivatives **2~7, 8-1** and **9-2** in hexane were measured and are summerized in Fig. 9. Evidently, the diolefin derivative **4** and C39 peridinin derivative **7** showed the longer max than that of peridinin. The max value in polyene chain modified derivatives **5**-**7** increased almost 20 nm per one olefin unit added to the conjugated polyene. On the other hand, the olefin derivative **3**, having eight conjugated carboncarbon double bonds like peridinin, showed the shorter max than that of peridinin. The open-ring derivative also displayed a shorter max than peridinin (**1**) due to shorter effective -electron conjugated chain length, although the 9'E-olefin ester derivative **9-2** had the same conjugated carbon-carbon double bonds compared with peridinin. These results show that the allene and ylidenebutenolide group at least contribute to giving rise to the max value desirable for the marine organism to absorb light in the blue-green region of the visible spectrum.

Fig. 8. Stereochemical characteristics of ylidenebutenolide modified derivatives

compound and would keep the all-*trans* conformer suitable for incorporation into the

The maximum absorption wavelengths (max) in the electronic spectra of peridinin (**1**) and the synthesized derivatives **2~7, 8-1** and **9-2** in hexane were measured and are summerized in Fig. 9. Evidently, the diolefin derivative **4** and C39 peridinin derivative **7** showed the longer max than that of peridinin. The max value in polyene chain modified derivatives **5**-**7** increased almost 20 nm per one olefin unit added to the conjugated polyene. On the other hand, the olefin derivative **3**, having eight conjugated carboncarbon double bonds like peridinin, showed the shorter max than that of peridinin. The open-ring derivative also displayed a shorter max than peridinin (**1**) due to shorter effective -electron conjugated chain length, although the 9'E-olefin ester derivative **9-2** had the same conjugated carbon-carbon double bonds compared with peridinin. These results show that the allene and ylidenebutenolide group at least contribute to giving rise to the max value desirable for the marine organism to absorb light in the blue-green

Fig. 8. Stereochemical characteristics of ylidenebutenolide modified derivatives

protein to form the PCP complex.

region of the visible spectrum.

Fig. 9. Structure of synthesized peridinin derivatives and result of UV spectra in hexane


**3. Discussion**

Several preadipocytes culture systems by which cells are able to be maintained for several passages have been established so far. For example, human preadipocytes were cultured in a medium 199 or DMEM/F-12 medium supplemented with 10% fetal bovine serum (FBS) [10]. ADSCs from lipoaspirates were generally cultured in a DMEM medium containing 10% FBS [8,37]. However, we have noticed that such ADSCs, cultured in a medium containing 10% FBS, rapidly lost their growth potential and exhibited senescence-like morphology. Since fetal bovine serum is well-known to contain some components showing growth inhibitory effects [38], we attempted to find a serum-free culture condition suitable for ADSCs. Our medium was originally prepared for primate embryonic stem cells [39], and it significantly improved the growth of ADSCs in culture, which enabled us to examine their biological and physiological activities.

In HIV-infected patients, subcutaneous adipose-tissue damage is quite obvious among those receiving HAART [19–22]. In the current study, ADSCs were isolated from the less affected parts of the body of HIV-infected patients. However, the recovery rates of ADSCs from the lipoaspirates obtained from the HIV-infected patients were about one-tenth of those observed in HIV-uninfected patients, indicating that ADSCs obtained from those parts of body were notably damaged. Therefore, it was expected that physiological activity of ADSCs in those parts of the body was compromised. However, our present study clearly demonstrated that there was no detectable difference in the growth kinetics, saturation density, and cloning efficiency between ADSCs obtained from HIV-infected and HIV-uninfected patients (Table 2). We are able to conclude that ADSCs from HIV-infected patients are biologically normal. We then compared the potential of adipogenic differentiation of ADSCs, and we found that the formation of lipid droplets was completely normal in ADSCs obtained from HIV-infected patients, indicating that adipogenic conversion was not compromised in those ADSCs (Figure 2 and Table 3). The conclusion was also confirmed by the protein analysis in Figure 3, in which no difference was detectable in the expression of several proteins involved in adipogenesis. Thus, it is quite obvious that ADSCs from HIV-infected patients retain normal physiological activity. Since previous study has claimed that HIV-infection alone causes lipodystrophy through abrogation of mitochondrial function [32], we have examined whether ADSCs from HIV-infected patients show increased oxidative

stress levels or not. As shown in Figure 4, the results clearly showed no detectable change in oxidative stress level in all cases. While mitochondrial damage can occur in vivo, ADSCs isolated from the patients and expanded in culture might regain physiological mitochondrial function, suggesting that ADSCs used for therapy are better to allow time in culture to recover before transplantation.

Recent advances in plastic and reconstructive medicine have allowed autologous stem cell therapy [40–45]. As we recently reported [13], it is evident that autologous stem cell therapy is able to retrieve the abrogated function of skin. Furthermore, tissue regeneration using ADSCs involves indirect effects, which accelerate wound healing through secreting growth factors [46–52]. Thus, autologous ADSC therapy could be a promising solution for subcutaneous adipose-tissue damage, including lipodystrophy in the patients receiving HAART. So far, facial lipodystrophy has been recognized as a common side effect of HAART, and autologous fat grafting is an effective treatment modality. In this study, we proved that ADSCs derived from the patients receiving HAART retain sufficient physiological and biological activity for adipogenic differentiation. In this way, ADSCs from the HIV-infected patients are the ideal sources for autologous stem cell therapy for lipodystrophy. Although we should be cautious as a number of cases examined in this study was limited, ADSCs from the patients with lipodystrophy could have sufficient biological potentials, so that they could be used for autologous ADSCs-based regenerative therapy [53].