abstract: Production from a high pressure gas well at a high production-rate encounters the risk of operating near the choking condition for a compressible flow in porous media. The unbounded gas pressure gradient near the point of choking, which is located near the wellbore, generates an effective tensile stress on the porous rock frame. This tensile stress almost always exceeds the tensile strength of the rock and it causes a tensile failure of the rock, leading to wellbore instability. In a porous rock, not all pores are choked at the same flow rate, and when just one pore is choked, the flow through the entire porous medium should be considered choked as the gas pressure gradient at the point of choking becomes singular. This thesis investigates the choking condition for compressible gas flow in a single microscopic pore. Quasi-one-dimensional analysis and axisymmetric numerical simulations of compressible gas flow in a pore scale varicose tube with a number of bumps are carried out, and the local Mach number and pressure along the tube are computed for the flow near choking condition. The effects of tube length, inlet-to-outlet pressure ratio, the number of bumps and the amplitude of the bumps on the choking condition are obtained. These critical values provide guidance for avoiding the choking condition in practice. / Dissertation/Thesis / M.S. Mechanical Engineering 2013

This thesis addresses the experimental investigation of the cavitation phenomenon and its main consequences on the normal operation of a safety relief valve (SRV). More particularly, limitation of the mass flux discharged and alteration of the hydraulic fluid forces behavior is of main interest for the proper design and sizing of such devices. In nuclear or thermal engineering systems, the use of SRVs is mandatory since it represents the ultimate protection device before an accident occurs, caused by a sudden pressurization of the system. A careful design and sizing of the SRV is therefore essential. The complete understanding of the physics taking place in the flow through the valve is required to guaranty and optimize the security of the protected process.<p><p>In order to investigate the above effects of cavitation in a SRV, two different orifice sized valves (API 2J3 type and a transparent model based on an API 1 1/2G3 type) are tested in two different experimental facilities expressly built for this purpose. Instead of using a spring, the design of both valves allows the adjustment of the disc at any desired lift. Hence the static behavior of the valves is investigated. Both facilities, operating at different magnitude scales, allow the study of single phase and cavitating flow conditions required to properly determine the most important hydraulic characteristics, and access on any potential scaling effect between both sized SRVs. Experimental techniques used for the determination of the hydraulic characteristics include temperature, flow rate, fluid forces and pressure measurements both upstream and downstream the test sections. <p><p>Results show a similar influence of cavitation on the flow characteristics of both valves, minimizing any potential scaling effect. The liquid pressure recovery factor FL, which is normally used to identify a choked flow condition in a control valve, is experimentally determined for the first time in a SRV. The existence of a local minimum located at small openings of the lift indicates a change on the flow characteristics of both valves, which is related to the location of the minimum cross section of the flow that does not remain constant for every lift position. An extended experimental campaign is performed to analyse the effect of the blowdown ring adjustment located around the nozzle of the API 2J3 valve. Results confirm that the position of the ring has an important contribution for the hydraulic forces acting on the valve disc. <p><p>In the second part of the research, precise optical diagnostic techniques are successfully applied in the transparent valve to locally characterize the flow topology in a SRV experiencing cavitation. These results are innovative and enrich the experimental database available in the literature for the characterization and understanding of the flow physics in such devices. In a first configuration, high speed visualization is applied to observe qualitatively the flow pattern and the inception of liquid vaporization. Particle tracking results suggest that vapor bubbles are formed in the core of vortices detached from the shear layers attached to the valve. These rotational structures promote lower pressure regions allowing the liquid to vaporize. In the second configuration, particle image velocimetry is applied to extract the velocity field in both single phase and cavitating flow conditions. Results of PIV confirm the existence of a submerged jet just downstream the minimum section. This jet is characterized by two non-symmetric shear layers at its sides. Under cavitation conditions, PIV results confirm that vapor bubbles are formed preferentially inside the jet shear layers. The phenomenon of mass flux limitation caused by cavitation is reproduced at small openings of the valve and interaction with the flow topology is highlighted. It is observed that limitation of the flow occurs when the vena contracta is shifted towards the minimum geometrical section of the flow. Finally, instabilities of the flow downstream the critical section are investigated in the frequency domain by means of time resolved data. Results suggest that vortex shedding mechanism is dominated by a constant Strouhal number which is slightly affected by the valve opening. <p><p>In the last part of the research, the methodology used in water is extended and applied to cryogenic liquids. Two different geometries are investigated experimentally and numerically using water and liquid nitrogen as working fluids. Results suggest that both the flow coefficient (determined at single flow conditions), and the liquid recovery factor (used to identify choked flows), are independent on the fluid properties and therefore, an hydraulic similarity relation can be proposed.<p><p>This research project was carried out at the von Karman Institute for Fluid Dynamics (VKI), in Belgium, in close collaboration and with the funding of Centre Technique des Industries Mécaniques (CETIM) in France. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

The work deals with the design of a system of orifices for high pressure difference. The task of this work is to design a device for controlled discharge of steam-gas mixture from a volume compensator with an overpressure of 12,27 MPa to a tank with an overpressure of 0,02 MPa at a constant mass flow of 40 kg/h. The first part of the thesis contains the theory and also the basic principles of calculations. In the next part of the work, the theoretical properties of flow, such as the speed of sound in wet steam, are determined. This knowledge then serves the main goal of the work, namely to design a system of orifices to release steam-gas mixture from the volume compensator.

The labyrinth seal is a non-contact annular type sealing device used to reduce the internal leakage of the working fluid which is caused by the pressure difference between each stage in a turbomachine. Reducing the leakage mass flow rate of the working fluid through the labyrinth seal is desirable because it improves the efficiency of the turbomachine. The carry-over coefficient, based on the divergence angle of the jet, changed with flow parameters with fixed seal geometry while earlier models expressed the carry-over coefficient solely as a function of seal geometry. For both compressible and incompressible flows, the Reynolds number based on clearance was the only flow parameter which could influence the carry-over coefficient. In the case of incompressible flow based on the simulations for various seal geometries and operating conditions, for a given Reynolds number, the carry-over coefficient strongly depended on radial clearance to tooth width ratio. Moreover, in general, the lower the Reynolds number, the larger is the divergence angle of the jet and this results in a smaller carry-over coefficient at lower Reynolds numbers. However, during transition from laminar to turbulent, the carry-over coefficient reduced initially and once the Reynolds number attained a critical value, the carry-over coefficient increased again. In the case of compressible flow, the carry-over coefficient had been slightly increased if radial clearance to tooth width ratio and radial clearance to tooth pitch ratio were increased. Further, the carry-over coefficient did not considerably change if only radial clearance to tooth width ratio was decreased. The discharge coefficient for compressible and incompressible flows depended only on the Reynolds number based on clearance. The discharge coefficient of the tooth in a single cavity labyrinth seal was equivalent to that in a multiple tooth labyrinth seal indicating that flow downstream had negligible effect on the discharge coefficient. In particular, for compressible fluid under certain flow and seal geometric conditions, the discharge coefficient did not increase with an increase in the Reynolds number. It was correlated to the pressure ratio, Pr. Moreover, it was also related to the fact that the flow of the fluid through the constriction became compressible and the flow eventually became choked. At low pressure ratios (less than 0.7), Saikishan’s incompressible model deviated from CFD simulation results. Hence, the effects of compressibility became significant and both the carry-over coefficient compressibility factor and the discharge coefficient compressibility factor needed to be considered and included into the leakage model. The carry-over coefficient compressibility factor, phi, had two linear relationships with positive and negative slopes regarding the pressure ratios. This result was not associated with the seal geometry because the seal geometry ratios for each instance were located within the nearly same ranges. Further, the phi-Pr relationship was independent of the number of teeth regardless of single and multiple cavity labyrinth seals. The discharge coefficient compressibility factor, psi, was a linear relationship with pressure ratios across the tooth as Saikishan predicted. However, in certain flow and seal geometric conditions, Saikishan’s model needed to be modified for the deviation appearing when the pressure ratios were decreased. Hence, a modified psi-Pr relationship including Saikishan’s model was presented in order to compensate for the deviation between the simulations and his model.