<p>Pressure gain combustion is beneficial for engine cycle efficiency, compactness, and less emissions. In this disseration, two classes of fluid expansions systems were developed to harness power from the high-speed flow delivered by the pressure gain combustor: a compact expansion system and an efficiency expansion system. In addition, a new class of pressure probes for expansion systems is developed.</p> <p>A numerical methodology is carried out to design and characterize these expansion devices and measurement systems via steady and unsteady Reynolds Averaged Navier stokes simulations. Firstly, the compact expansion system is achieved by developing a supersonic axial turbine. Performance of the supersonic axial turbine exposed to fluctuations from a nozzle downstream of a rotating detonation combustor is assessed with an increased level of complexity, including time-resolved stator, time-resolved rotor, and time-resolved turbine stage characterization. Power extraction, damping of fluctuations, and loss budgeting are evaluated. Unsteady heat transfer assessment is performed to investigate the convective heat flux distribution and decomposition. A performance map is constructed to explore the operating limit. Afterwards, the efficient expansion system is achieved by retrofitting an existing subsonic axial turbine. Without redesigning turbine airfoils, the stator endwall contour was modified to integrate the subsonic axial turbine to a diffuser and a rotating detonation combustor. Performance of the retrofitted subsonic axial turbine exposed to fluctuations form a diffuser is evaluated at several frequencies, amplitudes and inlet Mach numbers, with an increased level of model fidelity, including unsteady stator alone, unsteady turbine stage with a reduced model, full unsteady turbine stage assessment. Turbine efficiency, damping of oscillations, and loss budgeting are assessed. A multi-step optimization strategy is utilized to enhance turbine efficiency by improving the endwall contouring. A performance map is created to examine the operating range. Finally, a new type of pressure probes was developed and angular calibration was performed. A whisker-inspired design enabled the reduction of the vortex shedding effect.</p>

This thesis is concerned with the calculation of the power turbine. This turbine should be used in the automatic drive of the compressor used for compression of natural gas in compressor stations. Flight engine aeroderivate from the Rolls-Roye company, type RB211-22B, was used as gas generator. The main aim of the thesis is to summarize of the base atributes of the combustion turbines and aeroderivates. They are used for automatic engine, application a thermodynamic calculation of the power turbine, for reaction stage and basic strength calculations.

Pulse detonation engines show potential to increase the efficiency of conventional gas turbine engines if used in place of the steady combustor. However, since the interaction of pressure pulses with the turbine is not yet well understood, a rig was built to compare steady flow with pulsing flow. Compressed air is used in place of combustion gases and pressure pulses are created by rotating a ball valve with a motor. This work accomplishes two main objectives that are different from previous research in this area. First, steady flow through an axial turbine is compared with full annular pulsed flow closely coupled with the turbine. Second, the error in turbine efficiency is approximately half the error of previous research comparing steady and pulsed flow through an axial turbine. The data shows that a turbine driven by full annular pressure pulses has operation curves that are similar in shape to steady state operation curves, but with a decrease in turbine performance that is dependent on pulsing frequency. It is demonstrated that the turbine pressure ratio increases with pulsed flow through the turbine and that this increase is less for higher pulsing frequencies. For 10 Hz operation the turbine pressure ratio increases by 0.14, for 20 Hz it increases by 0.12, and for 40 Hz it increases by 0.06. It is demonstrated that the peak turbine efficiency is lower for pulsed flow when compared with steady flow. The difference between steady and pulsed flow peak efficiency is less severe at higher pulsing frequencies. For 40 Hz operation the turbine efficiency decreases by 5 efficiency points, for 20 Hz it decreases by 9 points, and for 10 Hz it decreases by 11 points. It is demonstrated that the specific power at a given pressure ratio for pulsed flow is lower than that of steady flow and that the decrease in specific power is lower for higher pulsing frequencies. On average, the difference in specific power between steady and pulsed flow is 0.43 kJ/kg for 40 Hz, 1.40 kJ/kg for 20 Hz, and 1.91 kJ/kg for 10 Hz.

Pressure gain combustion is a form of combustion that uses pressure waves to transfer energy and generate a rise in total pressure during the combustion process. Pressure gain combustion shows potential to increase the cycle efficiency of conventional gas turbine engines if used in place of the steady combustor. However, one of the challenges of integrating pressure gain combustion into a gas turbine engine is that a turbine driven by pulsing flow experiences a decrease in efficiency. The interaction of pressure pulses with a turbine was investigated to gain physical insights and to provide guidelines for designing turbines to be driven by pulsing flow. An experimental rig was built to compare steady flow with pulsing flow. Compressed air was used in place of combustion gases; pressure pulses were created by rotating a ball valve with a motor. The data showed that a turbine driven by full annular pressure pulses has a decrease in turbine efficiency and pressure ratio. The average decrease in turbine efficiency was 0.12 for 10 Hz, 0.08 for 20 Hz, and 0.04 for 40 Hz. The turbine pressure ratio, defined as the turbine exit total pressure divided by the turbine inlet total pressure, ranged from 0.55 to 0.76. The average decrease in turbine pressure ratio was 0.082 for 10 Hz, 0.053 for 20 Hz, and 0.064 for 40 Hz. The turbine temperature ratio and specific turbine work were constant. Pressure pulse amplitude, not frequency, was shown to be the main cause for the decrease in turbine efficiency. Computational fluid dynamics simulations were created and were validated with the experimental results. Simulations run at the same conditions as the experiments showed a decrease in turbine efficiency of 0.24 for 10 Hz, 0.12 for 20 Hz, and 0.05 for 40 Hz. In agreement with the experimental results, the simulations also showed that pressure pulse amplitude is the driving factor for decreased turbine efficiency and not the pulsing frequency. For a pulsing amplitude of 86.5 kPa, the efficiency difference between a 10 Hz and a 40 Hz simulation was only 0.005. A quadratic correlation between turbine efficiency and corrected pulse amplitude was presented with an R-squared value of 0.99. Incidence variation was shown to cause the change in turbine efficiency and a correlation between corrected incidence and corrected amplitude was established. The turbine geometry was then optimized for pulsing flow conditions. Based on the optimization results and observations, design recommendations were made for designing turbines for pulsing flow. The first design recommendation was to weight the design of the turbine toward the peak of the pressure pulse. The second design recommendation was to consider the range of inlet angles and reduce the camber near the leading edge of the blade. The third design recommendation was to reduce the blade turning to reduce the wake caused by pulsing flow. A new turbine design was created and tested following these design recommendations. The time-accurate validation simulation for a 10 Hz pressure pulse showed that the new turbine decreased the entropy generation by 35% and increased the efficiency by 0.04 (5.4%).

The diploma thesis consists of a theoretical part, which deals with the description of reversing turbocharger and its components. The following part is devoted to calculating the radial-axial compressor and turbine. It also performs a calculation of gear box and characteristics of the turbine.

Afin de faire face aux fortes températures rencontrées par les composantsen aval de la chambre de combustion, des prélèvements d’air plus frais sont réalisésau niveau du compresseur. Cet air alimente les cavités en pied de turbine et refroidiles disques rotor permettant d’assurer le bon fonctionnement de la turbine.Ce manuscrit présente une étude numérique de l’effet de ces écoulements de cavitéau pied de la turbine sur ses performances aérodynamiques. Les phénomènesd’interaction entre l’air de cavité en pied de turbine et l’air de veine principal est unphénomène encore difficilement compris. L’étude de ces phénomènes est réalisée autravers de différentes approches numériques (RANS, LES et LES-LBM) appliquéesà deux configurations pour lesquelles des résultats expérimentaux s ont disponibles.Une première configuration en grille d’aube linéaire en amont de laquelle différentesgéométries d’entrefer (interface entre plateforme rotor et stator) et débits de cavitépouvaient être variés. Une seconde configuration annulaire composée de deux étagesde turbine comprenant les cavités en pied et plus proche d’une configuration industrielle.Les pertes additionnelles associées à l’écoulement de cavité sont mesurées etétudiées à l’aide d’une méthode basée sur l’exergie (bilans d’énergie dans l’objectifde générer du travail). / In order to deal with high temperatures faced by the components downstreamof the combustion chamber, some relatively cold air is bled at the compressor.This air feeds the cavities under the turbine main annulus and cool down the rotordisks ensuring a proper and safe operation of the turbine. This thesis manuscriptintroduces a numerical study of the effect of the cavity flow close to the turbine hubon its aerodynamic performance. The interaction phenomena between the cav-ity andmain annulus flow are not currently fully understood. The study of these phenomenais performed based on different numerical approaches (RANS, LES and LES-LBM)applied to two configurations for which experimental results are avail-able. A linearcascade configuration with an upstream cavity and various rim seal geometries(interface between rotor and stator platform) and cavity flow rate avail-able. Arotating configuration that is a two stage turbine including cavities close to realisticindustrial configurations. Additional losses incurred by the cavity flow are measuredand studied using a method based on exergy (energy balance in the purpose togenerate work).

The thesis comprises a collection of four papers with preceding summary and supplementary appendices. The core investigation solely is of experimental nature although reference and comparisons with numerical models will be addressed. The first admission stage in an industrial steam turbine is referred to as the control stage if partial admission is applied. In order to achieve high part load efficiency and a high control stage output it is routinely applied in industrial steam turbines used in combined heat and power plants which frequently operate at part load. The inlet flow is individually throttled into separate annular arcs leading to the first stator row. Furthermore, partial admission is sometimes used in small-scale turbine stages to avoid short vanes/blades in order to reduce the impact from the tip leakage and endwall losses. There are three main aspects regarding partial admission turbines that need to be addressed. Firstly, there are specific aerodynamic losses: pumping-, emptying- and filling losses attributed to the partial admission stage. Secondly, if it is a multistage turbine, the downstream stages experience non-periodic flow around the periphery and circumferential pressure gradients and flow angle variations that produce additional mixing losses. Thirdly, the aeromechanical condition is different compared to full admission turbines and the forcing on downstream components is also circumferentially non-periodic with transient load changes. Although general explanations for partial admission losses exist in open literature, details and loss mechanisms have not been addressed in the same extent as for other sources of losses in full admission turbines. Generally applicable loss correlations are still lacking. High cycle fatigue due to unforeseen excitation frequencies or due to under estimated force magnitudes, or a combination of both causes control stage breakdowns. The main objectives of this thesis are to experimentally explore and determine performance and losses for a wide range of partial admission configurations. And, to perform a forced response analysis from experimental data for the axial test turbine presented herein in order to establish the forced response environment and identify particularities important for the design of control stages. Performance measurements concerning the efficiency trends and principal circumferential and axial pressure distortions demonstrate the applicability of the partial admission setup employed in the test turbine. Findings reveal that the reaction degree around the circumference varies considerably and large flow angle deviations downstream of the first rotor are present, not only in conjunction to the sector ends but stretching far into the admission sector. Furthermore, it is found that the flow capacity coefficient increases with reduced admission degree and the filling process locally generates large rotor incidence variation associated with high loss. Moreover, the off design conditions and efficiency deficit of downstream stages are evaluated and shown to be important when considering the overall turbine efficiency. By going from one to two arcs at 52.4% admission nearly a 10% reduction in the second stage partial admission loss, at design operating point was deduced from measurements. Ensemble averaged results from rotating unsteady pressure measurements indicate roughly a doubling of the normalized relative dynamic pressure at rotor emptying compared to an undisturbed part of the admission jet for 76.2% admission. Forced response analysis reveals that a large number of low engine order force impulses are added or highly amplified due to partial admission because of the blockage, pumping, loading and unloading processes. For the test turbine investigated herein it is entirely a combination of number of rotor blades and low engine order excitations that cause forced response vibrations. One possible design approach in order to change the force spectrum is to alter the relationship between admitted and non-admitted arc lengths. / Denna sammanläggningsavhandling består av fyra artiklar och föregås av en sammanfattning med kompletterande bilagor. Kärnan av undersökningen är experimentell även om referenser och jämförelser med numeriska modeller förekommer där så bedöms lämpligt. Det första steget i en industriell ångturbin kallas reglersteg om partialpådrag tillämpas. Det används rutinmässigt i kraftvärmeanläggningar som ofta körs vid dellaster för att åstadkomma en hög dellastverkningsgrad och hög stegeffekt. Inloppsflödet delas in separata och individuellt strypreglerade pådragsbågar som leder till det första munstycksgittret. Ibland används partialpådrag i små turbiner för att undvika korta blad och på så sätt minska takläckage och ändväggsförlusternas inflytande på den totala förlusten. Det finns i huvudsak tre aerodynamiska/aeromekaniska egenheter som bör beaktas. Först det första är det speciella aerodynamiska förluster associerade till partialpådrag eller reglersteget: ventilations-, tömnings och fyllningsförluster. För det andra, om det är en flerstegsturbin påverkas också nedströms steg negativt av det asymmetriska flödet runt omkretsen som innefattar stora tryckvariationer och flödesvinkelvariationer. För det tredje är den aeromekaniska situationen speciell jämfört med ett fullpådraget steg. För partialpådrag existerar dynamiska krafter med snabba laständringar vid in och utpassering i pådragsbågen. Även om det existerar generella förklaringar i den öppna litteraturen angående förluster så har inte förlustmekanismerna utretts i samma omfattning jämfört med fullpådrag. Ingen generell förlustkorrelation finns. Utmattning på grund oförutsedda excitationsfrekvenser, underskattade kraftamplituder eller en kombination av båda orsakar reglerstegshaveri för ångturbinintressenter. De huvudsakliga målsättningarna med denna studie är att experimentellt utforska och bestämma prestanda och förluster för ett stort antal partialpådragskonfigurationer. Samt att genomföra en vibrationsanalys (relaterat till aerodynamiska kraftimpulser) utifrån mätdata från provturbinen avhandlad häri. Detta för att kartlägga de aeromekaniska förutsättningarna och om möjligt identifiera egenheter viktiga för konstruktion av reglersteg. Prestandamätningar rörande verkningsgradstrender och generella strömningsvariationer runt omkretsen bekräftar resultat från den öppna litteraturen och därmed demonstrerar dugligheten av den partialpådragskonfiguration som används i luftprovturbinen. Dessutom visar resultaten bland annat att reaktionsgraden varierar kraftigt runt omkretsen med stora variationer i rotorns utloppsvinkel inte enbart i anslutning till sektorändar utan långt in i pådragssektorn. Flödeskapacitetskoefficienten eller turbinkonstanten ökar med minskat pådrag och fyllningsprocessen genererar stora variationer i rotorns inloppsvinkel förknippade med höga förluster. Det är viktigt att beakta dellastförutsättningarna och verkningsgradsminskningen för nedströms steg. Genom att använda två pådragsbågar istället för en för ett givet pådrag av 52,4% minskar partialpådragsförlusterna för nedströmssteget med nästan 10 % vid designpunkten, härlett från mätningar. Samlade medelvärden från roterande instationära mätningar visar på en fördubbling av det relativa dynamiska trycket vid rotortömning jämfört med en opåverkad del av pådragsbågen. Vibrationsanalys (relaterat till aerodynamiska kraftimpulser) av mätdata avslöjar att partialpådrag orsakar en stor mängd kraftimpulser med låga varvtalsmultiplar, främst från ventilationen och påavlastningsprocesserna. För provturbinen så är det helt och hållet kombinationer mellan antalet rotorblad och dessa kraftimpulser som orsakar strömningspåverkade vibrationer. Ett möjligt tillvägagångssätt konstruktionsmässigt för att ändra kraftspektrumet är att ändra längförhållandet mellan pådragen och blockerad del. / QC 20120109

The present master thesis deals with the technologies for gas liquefaction focused on helium. The first part of the thesis contains a description of the history of liquefaction, production and usage of liquid helium, as well as the principles of liquefaction and cooling cycles. In the following part of the thesis is a detailed model of the liquefaction cycle for which radial-axial turbine wheels were designed. The last part of the thesis contains financial analysis of the suitability of using the expander with eddy current brake and the expander with an electric generator.

Global renewable energy requirements rapidly increase with the transition to a fossil-free society. As a result, intermittent energy resources, such as wind- and solar power, have become increasingly popular. However, their energy production varies over time, both in the short- and long term. Hydropower plants are therefore utilized as a regulating resource more frequently to maintain a balance between production and consumption on the electrical grid. This means that they must be operated away from the design point, also known as the best-efficiency-point (BEP), and often are operated at part-load (PL) with a lower power output. Moreover, some plants are expected to provide a spinning reserve, also referred to as speed-no-load (SNL), to respond rapidly to power shortages. During this operating condition, the turbine rotates without producing any power. During the above mentioned off-design operating conditions, the flow rate is restricted by the closure of the guide vanes. This changes the absolute velocity of the flow and increases the swirl, which is unfavorable. The flow field can be described as chaotic, with separated regions and recirculating fluid. Shear layer formation between stagnant- and rotating flow regions can be an origin for rotating flow structures. Examples are the rotating-vortex-rope (RVR) found during PL operation and the vortical flow structures in the vaneless space during SNL operation, which can cause the flow between the runner blades to stall, also referred to as rotating stall. The flow structures are associated with pressure pulsations throughout the turbine, which puts high stress on the runner and other critical parts and shortens the turbine's lifetime. Numerical models of hydraulic turbines are highly coveted to investigate the detrimental flow inside the hydraulic turbines' different sections at off-design operating conditions. They enable the detailed study of the flow and the origin of the instabilities. This knowledge eases the design and assessment of mitigation techniques that expand the turbines' operating range, ultimately enabling a wider implementation of intermittent energy resources on the electrical grid and a smoother transition to a fossil-free society. This thesis presents the numerical study of the Porjus U9 model, a scaled-down version of the 10 MW prototype Kaplan turbine located along the Luleå river in northern Sweden. The distributor contains 20 guide vanes, 18 stay vanes and the runner is 6-bladed. The numerical model is a geometrical representation of the model turbine located at Vattenfall Research and Development in Älvkarleby, Sweden. The commercial software ANSYS CFX 2020 R2 is used to perform the numerical simulations. Firstly, the draft tube cone section of the U9 model is numerically studied to investigate the sensitivity of a swirling flow to the GEKO (generalized kω) turbulence model. The GEKO model aims to consolidate different eddy viscosity turbulence models. Six free coefficients are changeable to tune the model to flow conditions and obtain results closer to an experimental reference without affecting the calibration of the turbulence model to basic flow test cases. Especially, the coefficients affecting wall-bounded flows are of interest. This study aims to analyze if the GEKO model can be used to obtain results closer to experimental measurements and better predict the swirling flow at PL operation compared to other eddy viscosity turbulence models. Results show that the near-wall- and separation coefficients predict a higher swirl and give results closer to experimentally obtained ones. Secondly, a simplified version of the U9 model is investigated at BEP and PL operating conditions and includes one distributor passage with periodic boundary conditions, the runner and the draft tube. The flow is assumed axisymmetric upstream of the runner, hence the single distributor passage. Previous studies of hydraulic turbines operating at PL show difficulties predicting the flow's tangential velocity component as it is often under predicted. Therefore, a parametric analysis is performed to investigate which parameters affect the prediction of the tangential velocity in the runner domain. Results show that the model predicts the flow relatively well at BEP but has problems at PL; the axial velocity is overpredicted while the tangential is underpredicted. Moreover, the torque is overpredicted. The root cause for the deviation is an underestimation of the head losses. Another contributing reason is that the runner extracts too much swirl from the flow, hence the low tangential velocity and the high torque. Sensitive parameters are the blade clearance, blade angle and mass flow. Finally, the full version of the U9 model is analyzed at SNL operation, including the spiral casing, full distributor, runner and draft tube. During this operating condition, the flow is not axisymmetric; vortical flow structures extend from the vaneless space to the draft tube and the flow stalls between the runner blades. A mitigation technique with independent control of each guide vane is presented and implemented in the model. The idea is to open some of the guidevanes to BEP angle while keeping the remaining ones closed. The aim is to reduce the swirl and prevent the vortical flow structures from developing. Results show that the flow structures are broken down upstream the runner and the rotating stall between the runner blades is reduced, which decreases the pressure- and velocity fluctuations. The flow down stream the runner remains mainly unchanged.

Turbomachinery forms the principal prime mover in the energy and aviation industries. Due to its size, improvements to this fleet of machines have the potential of significant impact on global emissions. Due to high gas temperatures in stationary gas turbines and jet engines, areas of flow mixing and cooling are identified to benefit from continued research. Here, sensitive areas are cooled through cold air injection, but with the cost of power to compress the coolant to appropriate pressure. Further, the injection itself reduces output due to mixing losses.A turbine testing facility is center to the study, allowing measurement of cooling impact on a rotating low degree of reaction high pressure axial turbine. General performance, flow details, and cooling performance is quantified by output torque, pneumatic probes, and gas concentration measurement respectively. The methodology of simultaneously investigating the beneficial cooling and the detrimental mixing is aimed at the cavity purge flow, used to purge the wheelspace upstream of the rotor from hot main flow gas.Results show the tradeoff between turbine efficiency and cooling performance, with an efficiency penalty of 1.2 %-points for each percentage point of massflow ratio of purge. The simultaneous cooling effectiveness increase is about 40 %-points, and local impact on flow parameters downstream of the rotor is of the order of 2° altered turning and a Mach number delta of 0.01. It has also been showed that flow bypassing the rotor blading may be beneficial for cooling downstream.The results may be used to design turbines with less cooling. Detrimental effects of the remaining cooling may be minimized with the flow field knowledge. Stage performance is then optimized aerodynamically, mixing losses are reduced, and the cycle output is maximized due to the reduced compression work. The combination may be used to provide a significant benefit to the turbomachinery industry and reduced associated emissions. / Strömningsmaskinen i dess olika variationer bildar den främsta drivmotorn inom kraftproduktion och flygindustrin. En förbättring av denna väldiga maskinpark har potentialen till betydande inverkan på globala utsläpp. Områden som identifierats kunna dra nytta av vidare forskning är ombandningsprocesser och kylning. Dessa områden är inneboende i stationära gasturbiner och jetmotorer på grund av de heta gaser som används. Kylning uppnås genom injektion av kall luft i kritiska områden och försäkrar därmed säker drift. Kylningen kommer dock till en kostnad. På cykelnivå krävs arbete för att komprimera flödet till korrekt tryck. Dessutom medför injektionen i sig förluster som kan härledas till omblandningsprocessen. Syftet med detta arbete är att samtidigt undersöka de fördelaktiga kylegenskaperna som nackdelarna med inblandning för att på så sätt bestämma den uppoffring som måste göras för en viss kylning. Alla förbättringar tros dock inte behöva föregås av en uppoffring. Om påverkan av kylningen på huvudflödet är välförstådd kan designen justeras för att ta hänsyn till denna förändring och minimera inverkan. Denna metodologi riktar sig mot ett särskilt kylflöde, kavitetsrensningsflödet, som har till uppgift att avlägsna het luft från den kavitet som uppkommer uppströms rotorskivan i ett högtrycksturbinsteg. Studien kretsar kring en turbinprovanläggning som möjliggör detaljerade strömningsmätningar i ett roterande turbinsteg under inverkan av kavitetsrensningsflödet. Högtrycksturbinsteget som används för undersökningen är av låg reaktionsgrad. Här kvantifieras generell prestanda genom mätning av vridmomentet på utgående axel. Flödesfältet kvantifieras med pneumatiska sonder, och kylningsprestandan predikteras genom gaskoncentrationsmätningar. Resultaten visar avvägningen och sambandet mellan turbinverkningsgrad och kylning i kavitet samt huvudkanal. Flödet mäts i detalj, och de effekter som kan förväntas uppkomma då ett turbinsteg utsätts för en viss mängd av kylflödet kvantifieras. De kvantitativa resultaten för det undersökta steget visar på en förlust i verkningsgrad på 1.2 procentenheter för varje procentenhet av kavitetsrensningsflödet i termer om massflödesförhållande. Samtidigt ses kyleffektiviteten öka med 40 procentenheter. Den lokala inverkan på flödesfältet nedströms rotorn för det undersökta steget är 2° i flödesvinken och en ändring på 0.01 i Machnummer för varje procentenhet av kylflödet. Dessa ändringar ses i form av ökad omlänkning och reducerad hastighet nära hubben, och vice versa omkring halva spännvidden. Inverkan av aktuell driftpunkt understryks genom arbetet. Det har också visats att ett läckage som kringgår rotorbladen i vissa kan fall ge fördelaktig kylning i områden nedströms. Denna kombinerade kunskap kan användas för design av turbiner med så låg mängd kylning som möjligt samtidigt som säker drift bibehålls. Den negativa inverkan av den återstående kylningen kan minimeras genom kunskapen om hur flödesfältet påverkas. Genom detta optimeras stegverkningsgraden aerodynamiskt, omblandningsförluster minimeras, och cykeleffekten maximeras genom det minskade kompressionsarbetet till följd av de reducerade kylmängderna. Kombinationen kan ge en betydande förbättring för turbinindustrin och minskade utsläpp. / <p>QC 20171129</p>