**9. Conclusions**

*Single Port Gynecologic Laparoscopic and Robotic-Assisted Surgery*

prophylactic surgery.

through this approach.

**8. Oncology applications**

**8.1 Endometrial cancer**

**8.2 Ovarian cancer**

**8.3 Cervical cancer**

entering the pouch of Douglas will be low.

**7.5 Non-gynecologic procedures**

and a pelvic washing for cytology can be obtained. In standard transvaginal surgery for adnexectomy adequate visualization to safely remove the entire tube and ovary is not always possible. The vNOTES approach also avoids an abdominal scar for a

In most circumstances laparoscopic appendectomy is a relatively straightforward procedure and can be safely accomplished by a vNOTES approach. Abdominal wall adhesions can be visualized and safely taken down which may alleviate some patients' symptoms of abdominal discomfort. Small umbilical hernias can be closed primarily or repaired with mesh against the abdominal wall

Women with endometrial cancer are often obese and have multiple medical comorbidities. There are many reports of performing transvaginal hysterectomy on those patients who may not tolerate an abdominal procedure. However, that approach does not always permit visualization and removal of the tubes and ovaries. Nor does it allow for sampling of the lymph nodes. VNOTES permits removal of the tubes and ovaries, a pelvic washing can be performed, the entire abdomen can be explored, and lymph nodes can be removed. Multiple reports in the literature document the ability to perform Sentinel lymph nodes by this approach as well as pelvic lymphadenectomy and even aortic lymphadenectomy [13–16]. Given that the recommendation currently for staging endometrial cancer is to utilize a minimally invasive technique, vNOTES can provide an additional method to achieve this goal.

In general ovarian cancer debulking is not performed with a minimally invasive

technique; however, there are exceptions. When patients are treated with neoadjuvant chemotherapy and have an excellent response, robotic or laparoscopic approach can be performed to remove any small residual disease. Early stage disease can also be staged by a minimally invasive route. A vNOTES approach can remove adnexal masses, the omentum, lymph nodes, and perform a full exploration of the abdominal cavity. The diaphragm can be reached with the appropriate instruments through the vagina to perform biopsies and visualization. Bulky disease in the pelvis would be a contraindication to a vNOTES approach as the likelihood of successfully

There are no reports in the literature currently on utilizing vNOTES to treat cervical cancer. Theoretically a radical vaginal hysterectomy could be performed with vNOTES and pelvic lymph nodes can be removed so it is only a matter of time before some surgeons become skilled enough at this technique to perform such an operation. While there is currently controversy regarding a possible decreased survival with a minimally invasive radical hysterectomy [17], data on a radical vaginal

approach does not appear to have a deleterious effect on outcome [18].

**82**

vNOTES has been shown to be a safe and feasible alternative approach to most gynecologic procedures. The technique is still in its infancy and is analogous to the early use of laparoscopy for advanced gynecologic surgery. There are distinct advantages with this approach including decreased pain, shorter recovery, and optimal cosmetics over standard laparoscopy. There is no doubt that vNOTES will be adopted by the surgical field. Instrumentation specific for vNOTES is beginning to be brought to the marketplace. Patient satisfaction with the technique will also drive more surgeons to these procedures. With vNOTES a gynecologist is able to offer the best aspects of laparoscopy with the ideal approach through the vagina.


**3. Results and Discussion**

#### *3.1. Metallographic Measurement*

Figure 1 shows the microstructures and the grain size distribution of the tested steels, with the microstructure parameters summarized in Table 2. It is clear from the data that both samples show a similar chemical composition, with very little variation between different elements, but different microstructures. The 300 steel shows a coarse-grained microstructure with an average grain size of *circa* 4265.9 μm2, whereas the 200 steel shows a fine-grained microstructure with an average grain size of *circa* 115.6 μm2.

**Figure 1.** Microstructure and the histogram showing the grain size number distribution of 200 (**a**–**c**) and 300 steels (**d**–**f**).

**Table 2.** Grain size analysis of the steels.

#### *3.2. Gravimetric Measurements*

Table 3 shows the corrosion rates of the samples obtained from the weight loss measurements after 24 h of immersion in the tested solution. It follows from the data that the *CR* of the sample with fine grains is approximately two times higher compared to the sample with coarse grains. The analysis of the chemical composition (Table 1) shows that both specimens have a similar composition, with very little variation in concentration of the alloying elements. It can be inferred that the small differences observed in microalloying do not affect the corrosion rate of the metal and that the difference in the corrosion rate is therefore related to the microstructure. Similar results were also reported in [8,11,12,14–16,18]. Onyeji et al. [8] reported that the corrosion behavior of two X65 steels with identical chemical composition but different microstructures varied. The authors observed that the coarse-grained steel showed higher corrosion resistance compared to the steel with a fine grained microstructure. The authors suggested that this behavior was attributed to the enhanced reactivity of the surface after the grain refinement, which causes a preferential dissolution of the grains.

**Table 3.** Weight loss and corrosion rate of the steels after 24 h of immersion time.


3.4.3. Reference Approach

As reference experiment for direct comparison in the same population, a recent sEMG-based approach was used [14]. In this reference approach only sEMG signals were used to train the network. Similarly to the KEMG approach, each sEMG signal was split into 20-sample windows. A chronological

sequence of 160-sample vectors was created, where each vector included the eight synchronized 20-sample windows from the sEMG signals of the eight muscles (four for each leg). In details, the first sample of the first 160-sample vector of the sequence was the first sample of the sEMG signal from the muscle 1 (TA, right leg), the second sample of the first 160-sample vector was the first sample of the EMG signal from the muscle 2 (GL, right leg), and so on up to the eighth signal (MH, left leg). Labeling was performed as in the previous approaches. This approach is referred to as the 'Reference approach'. As reported in [14], this approach has been previously validated versus a feature-based method, described in [13].


**4. Discussion**

Perhaps, the most important results of the study are that in systems with minimum and maximum concentrations of inorganic ions, only analogs of the phosphate renal stone mineral phases were observed, while calcium oxalates were obtained under given conditions only with an increase in the concentration of oxalate ions up to the oxalatouria values, both in experiments with bacteria and without them. This result is in general agreement with the literature data on model crystallization experiments in the human urinary system [21,27,31]. Thus, according to the thermodynamic calculations and experiments in systems that simulate composition of the physiological liquid, calcium oxalates are formed in much smaller quantities than what is actually observed during pathogenic processes in the human body. Moreover, the weddellite phase (calcium oxalate dihydrate) does not form at all [31]. Introduction of bacteria and protein (ovalbumin) to the system leads to a similar result in all the experiments, increasing the portion of weddellite and increasing the amount of calcium oxalates in general. It should be also noted that, according to the unit cell parameters of weddellite crystals which are formed in the presence of bacteria, the amount of "zeolite" H2O molecules (x) falls into a rather narrow range of values, whereas those in the structures of weddellite crystals from human renal stones vary much more (from 0.13 to 0.37 p.f.u.).

According to our data, all bacteria initiate the nucleation of calcium oxalates and promote the crystallization of metastable calcium oxalate dihydrate (weddellite) in the oxalate system (containing only Ca2<sup>+</sup> and [C2O4] 2– ions). The initiation of calcium oxalate nucleation in the presence of bacteria is in agreement with the results of some recent studies, which describe an increase in the number of calcium oxalate crystals and their size in the presence of bacteria [32].

As it was shown by the results of phosphate crystallization experiments, the addition of bacteria and nutrient media leads to a change in the phase composition of the precipitate and to the shift of the phosphate phase's formation boundaries (Figures 3 and 4). The addition of the MHB medium to the model solution with the minimum concentration of inorganic impurities led to the disappearance of octacalcium phosphate and whitlockite, followed by the formation of brushite and rare struvite occurrences. The same addition to the model solution with the maximum concentration of inorganic impurities led to the crystallization of apatite, along with brushite and struvite, and to the significant shift of brushite and apatite formation areas toward higher pH values of the solution (~7.0).

The addition of the MPB medium to the model solution with a minimum concentration of inorganic impurities led to the formation of brushite and whitlockite and, in addition, crystallization of struvite was detected at a pH of 7.26, so the shift in the struvite phase formation boundary in this system moved toward being significantly more acidic. The brushite phase was observed in this system in a narrower pH range around 7.06. Since brushite did not form in experiments without organic additives at such a high pH, this suggests that the boundary of its formation expanded to the more alkaline side. The same addition to the model solution with the maximum concentration of inorganic impurities did not lead to any change in the phase composition of the synthesized products. At the same time, it can be stated that the boundary of the brushite formation area has shifted to the more alkaline region of solutions and the boundary of the struvite formation area shifted to the more acidic region (pH of 6.96).

The addition of bacteria to the appropriate media led to additional changes in the composition of the precipitates (Figures 3 and 4). Thus, in the syntheses with minimal concentrations of inorganic impurities, the appearance of *Escherichia coli* and *Pseudomonas aeruginosa* in an MHB medium led to the formation of struvite and shifted its starting crystallization boundary to the more acidic region (pH of 7.05). Although struvite was initially present in the synthetic products, the appearance of bacteria in the MHB medium contributed to the displacement of its crystallization area to the more acidic region. The effect of *Escherichia coli* and *Staphylococcus aureus* bacteria on the crystallization of brushite was also well demonstrated in systems containing MHB; the shift of the brushite initial crystallization area occurred toward the more alkaline region. The effect of the bacteria addition on the crystallization of apatite was clearly visible in the MPB medium; the appearance of bacteria promoted crystallization of apatite and shifted its formation boundary to the more acidic region (pH of 6.72).

The change in the pH values of the solution during the biomimetic syntheses process occurred in different directions, due to both the crystallization process of various phases and the effect of a certain protein medium type and all types of bacteria addition. The decrease in pH in systems that modeled urine using inorganic components can be explained by the result of phosphate phase crystallization, while an increase in systems with bacteria can be explained by the influence of metabolic products. The presence of urease-producing bacteria such as *Pseudomonas aeruginosa*, *Klebsiella pneumoniae* and *Staphylococcus aureus* in urea led to an increase in pH [11,12].

The displacement of struvite crystallization boundaries obtained in the experiments, which led to its intensive formation, once again underlines the involvement of bacteria in the formation of "infectious" renal stones, described in a number of works [3,12]. At the same time, the expansion of the brushite crystallization area boundaries and the crystallization of apatite, as well as the formation of weddellite in the oxalate system, shows that the influence of the presence and function of bacteria in the crystallization medium was not only limited to the alkalization of the urine and the formation of ammonium ions, but significantly affected the types of growing mineral phases and the size of their crystallization areas with natural variations in urine pH.


2. Enhanced nonlinear dynamic model

The structure and operation of the above-mentioned ENDM are illustrated by Figure 1. Modules 1–4 constitute SDCM of an engine component, compressor or turbine. Module 5 presents an initial engine model, which, in conjunction with SDCM, presents the enhanced nonlinear model. Only one component is presented on this scheme for simplicity. The software of ENDM includes SDCMs for all the components where the dynamic clearance effect is significant. The enhanced model has been developed for a low-bypass two-spool turbofan engine of a maneuverable aircraft. All simplified relations for the clearance model were obtained through exhaustive calculations in ANSYS with the solid models of engine stator and rotor hot parts, namely disk, blade, and casing. The below description of the clearance model is given for a high-pressure turbine (HPT) of this engine as a component example.

The initial nonlinear dynamic model includes the dynamics of two engine rotors. The corresponding differential equations are solved through their integration by an iterative procedure. In each step, the corrections to state variables (rotation speeds) are obtained and all engine variables are renewed. The enhanced engine model

Figure 1. Structure of the enhanced nonlinear dynamic model.

conserves this iterative character. At an actual step, the variables computed by NDM are used in SDCM to calculate a new tip clearance and corrections to component performances. The modified performances are employed at the next step. In this way, as with real engine dynamics, ENDM uses component performances that are dynamically changed.

Blocks 1.1–1.4 for the stator and Blocks 2.1–2.4 for the rotor illustrate what happens with heated parts (disk, blade, and casing) and tip clearances when engine operating mode dynamically changes. After the mode change, the gas path variables calculated by NMM (Block 5) begin to vary producing the change of heat exchange boundary conditions outside of the heated parts (Blocks 1.1 and 2.1). Because of heat accumulation or loss, the temperature state (distribution of metal temperature) of HPs begins to change (Blocks 1.2 and 2.2). Elevated temperatures of HP cause its thermal expansion. As the HP temperature state has a delay relative to the engine mode change, the corresponding displacement (Blocks 1.3 and 2.3) varies with a delay as well. The knowledge of the temperature state also allows us to correctly consider the action of forces on the HP radial displacements. As shown in [21], for a disk and blade, significant displacements are caused by a centrifugal force, while a pressure force is the most influencing for a casing. These forces are considered in Blocks 1.4 and 2.4 accordingly. When an engine operating point is changing, the force applied to HP changes as well, and the force-induced displacement reacts immediately. However, the engine mode variation also means the change of the heat exchange boundary conditions resulting in other temperature state, other metal elasticity, and an additional change of the displacement. Thus, the force-induced displacement has a static component that immediately reacts on the engine mode and a dynamic component that reacts with a delay. In this way, the total radial displacements of the surfaces that form a tip clearance have a complex dynamic behavior.

The calculation of a dynamic clearance change (see Module 3), which is necessary to evaluate the change in a component performance, is based on simple relations. An actual dynamic tip clearance δ that is a function of transient time can be expressed through a clearance δ0 of a cold turbine and total displacements uC, uD, δB of the casing, disk, and blade accordingly, resulting in

$$\delta = \delta\_0 + \mathbf{u}\_{\mathbb{C}} - (\mathbf{u}\_{\mathbb{D}} + \mathbf{u}\_{\mathbb{B}}) \tag{1}$$

where L is a blade length. Figure 2 illustrates this relation.

depending on the construction of a modeled engine and its component.

simulation of the HP displacements is described in the next section.

3. Finite element-based displacement simulation

these conditions and loads.

159

3.1 Thermal boundary conditions and mechanical loads

of a transient process according to an expression:

Advanced Nonlinear Modeling of Gas Turbine Dynamics

DOI: http://dx.doi.org/10.5772/intechopen.82015

Turbine efficiency losses vs. an increasing tip clearance.

Figure 2.

the effect of dynamically varying radial clearances.

Therefore, Module 4 computes the corrected component efficiency at each point

where ηst is the efficiency at an equivalent steady state and k is the coefficient

Since Module 5 employs the corrected efficiencies of all the engine components as input parameters, the engine variables simulated by NDM take into consideration

As can be seen from the above description, the equations of Modules 3 and 4 are

As shown in Figure 1 and described in Section 2, the displacements of the heated parts depend on thermal boundary conditions and mechanical loads applied. Shown in Figure 3, the design scheme of the disk, which is the most complex HP, illustrates

The boundary conditions are set by an external air and gas temperature T and heat transfer coefficient α at the disk surface. Since these conditions considerably vary at different parts of the surface, it is broken down into 24 sections with constant temperatures Ti and coefficients αi. At one engine steady state called a

simple and do not need additional explanations. A nonlinear dynamic model of Module 5 is not simple, but it does not need additional description because this type of gas turbine models is well described in literature. However, Modules 1 and 2 and their blocks were presented in this section in a schematic form necessary for a general understanding of the enhanced NDM. As described before, in these modules, the displacements of the heated parts are calculated. To know how these displacements depend on external factors, the displacements were simulated in ANSYS by creating the solid model of each HP and by applying the finite element method to determine the HP stress-stain state. By multiple numerical experiments of this type, the simplified relations between the displacement and external dynamic factors were formed and included in Modules 1 and 2. This ANSYS-based

η ¼ ηst � kΔδ (5)

Since the HPT performance map used in NDM corresponds to the turbine parts completely warmed up at steady states, the necessary dynamic correction of the performance will depend on a difference Δδ between a dynamic clearance δ and a static clearance δst. Let us express the static clearance in the form of Eq. (1) but using static displacements of HPs. This yields:

$$\boldsymbol{\delta}^{\rm st} = \boldsymbol{\delta}\_0 + \mathbf{u}\_{\rm C}^{\rm st} - \left(\mathbf{u}\_{\rm D}^{\rm st} + \mathbf{u}\_{\rm B}^{\rm st}\right) \tag{2}$$

In this way, the dynamic clearance change is written by:

$$
\Delta \mathsf{S} = \left( \mathbf{u}\_{\mathrm{C}} - \mathbf{u}\_{\mathrm{C}}^{\mathrm{st}} \right) - \left( \mathbf{u}\_{\mathrm{D}} - \mathbf{u}\_{\mathrm{D}}^{\mathrm{st}} \right) - \left( \mathbf{u}\_{\mathrm{B}} - \mathbf{u}\_{\mathrm{B}}^{\mathrm{st}} \right) \tag{3}
$$

Using the clearance change Δδ as an input parameter, Module 4 corrects the component efficiency η because it is known that just this performance is affected by an increased clearance. Paper [23] shows that a turbine efficiency loss Δη is linearly dependent on a relative clearance change:

Δδ ¼ Δδ=L (4)

Advanced Nonlinear Modeling of Gas Turbine Dynamics DOI: http://dx.doi.org/10.5772/intechopen.82015

#### Figure 2.

conserves this iterative character. At an actual step, the variables computed by NDM are used in SDCM to calculate a new tip clearance and corrections to component performances. The modified performances are employed at the next step. In this way, as with real engine dynamics, ENDM uses component performances that

Blocks 1.1–1.4 for the stator and Blocks 2.1–2.4 for the rotor illustrate what happens with heated parts (disk, blade, and casing) and tip clearances when engine operating mode dynamically changes. After the mode change, the gas path variables calculated by NMM (Block 5) begin to vary producing the change of heat exchange boundary conditions outside of the heated parts (Blocks 1.1 and 2.1). Because of heat accumulation or loss, the temperature state (distribution of metal temperature) of HPs begins to change (Blocks 1.2 and 2.2). Elevated temperatures of HP cause its thermal expansion. As the HP temperature state has a delay relative to the engine mode change, the corresponding displacement (Blocks 1.3 and 2.3) varies with a delay as well. The knowledge of the temperature state also allows us to correctly consider the action of forces on the HP radial displacements. As shown in [21], for a disk and blade, significant displacements are caused by a centrifugal force, while a pressure force is the most influencing for a casing. These forces are considered in Blocks 1.4 and 2.4 accordingly. When an engine operating point is changing, the force applied to HP changes as well, and the force-induced displacement reacts immediately. However, the engine mode variation also means the change of the heat exchange boundary conditions resulting in other temperature state, other metal elasticity, and an additional change of the displacement. Thus, the force-induced displacement has a static component that immediately reacts on the engine mode and a dynamic component that reacts with a delay. In this way, the total radial displacements of the surfaces that form a tip clearance have a complex

The calculation of a dynamic clearance change (see Module 3), which is necessary to evaluate the change in a component performance, is based on simple relations. An actual dynamic tip clearance δ that is a function of transient time can be expressed through a clearance δ0 of a cold turbine and total displacements uC, uD, δB

Since the HPT performance map used in NDM corresponds to the turbine parts completely warmed up at steady states, the necessary dynamic correction of the performance will depend on a difference Δδ between a dynamic clearance δ and a static clearance δst. Let us express the static clearance in the form of Eq. (1) but

C � ust

Using the clearance change Δδ as an input parameter, Module 4 corrects the component efficiency η because it is known that just this performance is affected by an increased clearance. Paper [23] shows that a turbine efficiency loss Δη is linearly

D þ ust B

D � uB � ust

δst ¼ δ0 þ ust

C � uD � ust

In this way, the dynamic clearance change is written by:

Δδ ¼ uC � ust

δ ¼ δ0 þ uC � ð Þ uD þ uB (1)

(2)

(3)

B

Δδ ¼ Δδ=L (4)

of the casing, disk, and blade accordingly, resulting in

using static displacements of HPs. This yields:

dependent on a relative clearance change:

158

are dynamically changed.

Aerospace Engineering

dynamic behavior.

Turbine efficiency losses vs. an increasing tip clearance.

where L is a blade length. Figure 2 illustrates this relation.

Therefore, Module 4 computes the corrected component efficiency at each point of a transient process according to an expression:

$$
\boldsymbol{\eta} = \boldsymbol{\eta}^{\text{st}} - \mathbf{k} \Delta \overline{\boldsymbol{\delta}} \tag{5}
$$

where ηst is the efficiency at an equivalent steady state and k is the coefficient depending on the construction of a modeled engine and its component.

Since Module 5 employs the corrected efficiencies of all the engine components as input parameters, the engine variables simulated by NDM take into consideration the effect of dynamically varying radial clearances.

As can be seen from the above description, the equations of Modules 3 and 4 are simple and do not need additional explanations. A nonlinear dynamic model of Module 5 is not simple, but it does not need additional description because this type of gas turbine models is well described in literature. However, Modules 1 and 2 and their blocks were presented in this section in a schematic form necessary for a general understanding of the enhanced NDM. As described before, in these modules, the displacements of the heated parts are calculated. To know how these displacements depend on external factors, the displacements were simulated in ANSYS by creating the solid model of each HP and by applying the finite element method to determine the HP stress-stain state. By multiple numerical experiments of this type, the simplified relations between the displacement and external dynamic factors were formed and included in Modules 1 and 2. This ANSYS-based simulation of the HP displacements is described in the next section.