]. .. , 15 3 Engineering design workflow. Design proposals are rapidly evaluated using simulations with the objective of identifying the most promising candidates. These selected designs are tested and, if proved satisfactory, turned into operational prototypes. Otherwise, the experience is used to suggest improved designs. The numerical models, validated with test setups, and the test setups themselves are methods used during the design process, Drill bits used for drilling processes rely on mechanical face seals, 2001.

. , Phenomena governing face seal behaviour and their interactions

. , Forces applied to the flexibly mounted element of a face seal: closing forces left, opening forces right. Drawing adapted from, 2002.

. , Outside pressurized mechanical face seal with B < 1

. , Outside pressurized mechanical face seal with B > 1

. , Total torque over film thickness in number of Sq and for various friction coefficients using equations 1.1.4 and

. , Leakage over film thickness in number of Sq using equation 1.1.1

. , Stribeck curve showing the evolution of the overall seal friction coefficient as function of the duty parameter

. Zhang, Misaligned face seal, 2010.

, Left: cross section detailing the heat pipe in the stationary ring, p.31, 2014.

. , View of the wavy-tilt-dam face seal, 1989.

. Djamai, Face seal with notches simulated in, 2010.

, Surface sample used to determine the flow factors in, p.35, 1978.

. .. Model-building-workflow,

. , Phenomena governing face seal behaviour and their interactions

, Equations to be solved on the stator domain, ? s , film domain, ? f , and rotor domain ? r, p.38

, Schematic of a face seal, without misalignment (left), with misalignments ? r , ? s (right), p.39

, Example of a face seal with radii position, flexibly mounted element on the left, p.42

, Schematic of a face seal showing the forces applied to the flexibly mounted part, p.42

.. .. , 43 2.10 The true surface height is defined by h t , the average surface defined by h is considered when solving the Reynolds equation (drawing from, p.45, 1978.

, Overview of the input/output relations of the governing equations. Thick arrows indicate outputs, thin arrows inputs. The variables in blue correspond to the performance of the face seal, vol.52

. , Comparison of the acceleration predictions using implicit Euler second order, implicit Euler third order, and Newmark

. , Comparative relative error of acceleration with implicit Euler second order

. , Workflow of the face seal numerical model

. , Schematic of a face seal showing the inner and outer radius, r i , r o , face centre distance C o , coning angle ? and inner and outer pressures p i , p o

. , Comparison of the relative misalignment for various radius ratios predicted by the present model and the model of

. , Relative error on relative misalignment predicted by the present model and the analytical model for various radius ratio

. , Results of the present model in blue, results published in [Person et al., 1997] in black. The error bars correspond to the reading error

, Comparison of the face centre distance, minimum film thickness, and stator misalignment over time. The results of the present model are in full lines, the results published in [Tournerie and Frene, 1984], case 6, as dots. The error bars correspond to the reading error, p.76

, Comparison of the face centre distance, minimum film thickness, and stator misalignment over time. The results of the present model are in full lines; the results published in [Tournerie and Frene, 1984], case 8, as dots. The error bars correspond to the reading error, p.77

. .. , 78 3.10 Relative error on the radial temperature increase for various rotational speeds, p.78

. , Comparison of the film thickness increase for various rotational speeds

. , Relative error on the film thickness for various rotational speeds

. , Comparison of the radial temperature increase for various surrounding temperatures and associated fluid viscosities

. , Relative error on the temperature increase for various temperatures

. , Comparison of the film thickness for various surrounding temperatures and associated fluid viscosities

. , Relative error on the film thickness for various temperatures

. , Comparison of the temperature evolution predicted by the present model and the published results for various values of acceleration

. , Comparison of the evolution of the dissipated power predicted by the present model and the published results for various values of acceleration

. .. , Comparison of the radial temperature increase for various speeds for the face seal of, p.82

. , Test setup and its main elements

. Schematic and . .. Holder, , vol.87

. , Schematic of the face seal, vol.87

, Insertion of a rod inside the bellows to measure its position and infer the oil volume, p.89

. , outer (bottom) pressure sensor assembly fitted on the face seal holder. Right: exploded view of the outer pressure sensor assembly, Pressure sensor assembly. Left: view of the inner (top) and

, Red dashed line: pulse reaching the outer seal radius

. , Blue dashed line: pulse reaching the inner seal radius

. , Illustration of the differential pressure (black) resulting from delay of 1.57 ms between the inner and outer pressure (curve constructed using the equations of section 4.3.6)

. , Measurement of inner and outer pressure during pressure pulses at ±15 bar, at 12 Hz (top graph) and resulting pressure difference (bottom graph). The inner and outer pressure signals are filtered with a low pass filter of cutting frequency 35 Hz

. , Measurements of inner and outer pressure during pressure pulses at ±15 bar, at 12 Hz and computation of instantaneous delay at each extremum (black dots). The dashed black line corresponds to the average delay

. , Geometry of the face seal of interest

. , Schematic of the face seal and its surroundings

. , Temperature increase (colour map) in the face seal at reference conditions with isotherms (lines) and deformations magnified 1000 times

, Radial film temperature and film thickness profiles of the face seal at reference conditions, p.102

. , Radial distributions of the contact and fluid pressure contributions for the face seal at reference conditions

. , Convection coefficient for oil, water and resulting face seal leakage and maximum fluid temperature increase for various correlations of convection coefficient

. , Impact of the surface asperity standard roughness with ? = 1.78 µm

. , 107 5.10 Impact of the operating temperature on the performance of the reference face seal, p.108

. , Impact of the rotational speed on the performance of the reference face seal

. , Impact of the spring force on the performance of the reference face seal

. , Impact of the acceleration on the dissipated power, torque, leakage, maximum temperature increase, minimum and maximum film thickness

, Leakage and torque of the reference face seal for various numbers of nodes at the interface, p.112

. , on the mass flows (middle graph), minimum film thickness and maximum contact pressure (bottom graph)

. , Evolution of the film thickness (left), fluid pressure (middle) and contact pressure (right) of the reference face seal during pressure pulses

. , Radial film fluid pressure during pulses at various time instants

. , Radial film thickness profile during pulses at various time instants

. .. , 117 5.20 Illustration of the variation of ? r0 (t j )/V (t j ) (eq. 5.3.2) when the water travels 0%, 23% and 72% of the sealing dam (from left to right)

, Impact of the surface wear on the minimum film thickness and maximum contact pressure, p.120

. , 124 5.28 Evolution of the film thickness (left), fluid pressure (middle) and contact pressure (right) during the seal rotation when the rotor has 3 mrad misalignment

. , 126 5.30 Impact of the rotor misalignment ? r on the maximum contact pressure and minimum film thickness, Impact of the misalignment on the mass flows entering and exiting the seal at the outer (top) and inner (bottom) radii

. , Pressure boundary condition, mass flows at the inner and outer radius, percentage seal volume travelled, minimum film thickness and maximum contact pressure for a face seal with a rotor misalignment of 3.5 mrad

. .. , 130 5.33 View of a face of the face seal, left: rotor, right: stator

. , Circumferential height profile taken at the mean radius of a face of a face seal

. , Fixed position of the stator (black), position of the rotor when its lobes face the stator valleys (blue), position of the rotor after 45 degrees rotation (green) and after 90 degrees rotations (red). The distance between the rotor and stator is arbitrary, View of the position of the rotor and stator lobes as the rotor rotates

. , Evolution of the mass flow, film thickness and maximum contact pressure for the reference face seal with waviness

, There is a 45 degrees rotation counter-clockwise between each row of figures, starting from the top row, vol.135

. , Composition of the mass flows for the reference face seal with a waviness defect of 0.5 µm on the rotor and 0.4 µm on the stator

. , Simulation of the impact of the flatness defect on the leakage for the reference face seal (test 5 was presented in table 5.14)

. , Simulation of the impact of the flatness defect on the maximum water ingression for the reference face seal

. , Comparative impact of the average film thickness due to face waviness and surface roughness on the leakage

. , Maximum contact force as a function of average flatness defect

. , Mass flows, percentage of seal volume travelled, maximum contact pressure and minimum film thickness for the reference face seal with a waviness defect of 0.4 µm (stator) and 0.5 µm (rotor) operating with pressure pulses

. , Mass flows, percentage of seal volume travelled, maximum contact pressure and minimum film thickness for the diamond face seal of waviness 3.5 µm (stator) and 5.47 µm (rotor) operating with pressure pulses

. , From left to right: face position, rotation, axial translation, first misalignment angle, second misalignment angle

. , Configuration of two surfaces in relative motion

A. ;. , Contact pressure over face distance for various values of contact parameters, p.155

. , A.4 Impact of the number of nodes on the predicted relative misalignment and associated simulation time

. , Impact of the number of angular degrees covered by the rotor per iteration on the predicted relative misalignment and phase angle

. .. Seal, 106 5.9 Impact of the surface roughness standard deviation Sq and correlation length ? on face seal performance

, Summary of impact of uncertainty in the main variables on seal performance predictions, p.108

. , Temperature dependence of the physical parameters

. , Summary of impact of the operating conditions and design parameter on face seal performance predictions

. , Parameters to emulate thermo-mechanical deformations and thermal effects for the face seal of reference

. , First set of experimental results: Impact of pressure pulses and surface wear (absence of data indicated by ? )

. , Water in oil increase for the first set of experiments with pressure pulses

. , Parameters for the simulations of the reference face seal with emulated thermo-mechanical deformations

, Second set of experimental data: Impact of rotor misalignment (absence of data indicated by ? ), p.122

. , Water in oil increase for the first and second set of experiments with rotor misalignment and pulses

. , Dynamic parameters used for the simulations with a misaligned rotor

. , Simulation results showing the impact of misalignment and pulses on the water entry expressed in percentage of fluid volume travelled

. , Simulation results showing the impact of misalignment and pulses on the maximum contact pressure

, Third set of experimental data: Wavy diamond face seal (absence of data indicated by ? ), p.131

. , Experimental average increase of water in oil content per hour for the wavy diamond face seal prototype

. , Parameters for the simulations of the reference face seal with emulated thermo-mechanical deformations

. , Material properties of the face seal prototype

. , Average leakage for the wavy diamond face seal prototype

. , Water in oil increase for the first and second set of experiments with rotor misalignment and pulses

. , Experimental average increase of water in oil content per hour for the wavy diamond face seal prototype

. , Average leakage for the wavy diamond face seal prototype

, A.1 Parameters of the face seal used for the comparison with, p.159, 1997.

. , Values obtained with the present model to generate curve 3

, A.3 Parameters of the face seal used for the verification with [Tournerie and Frene, p.160, 1984.

, Values obtained with the present model to generate bottom graph of figure 3.8, p.160

, A.5 Parameters of the face seal used for the verification with Brunetì ere, p.161, 2003.

A. , Values obtained with the present model and used to generate curve 3.9

, A.7 Parameters of the face seal used for the comparison with, p.162

, A.8 Predictions of the present model for the comparison with

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