A Computational Fluid Dynamics Modified Bulk Flow Analysis for Circumferentially Shallow Grooved Liquid Seals

Pumping efficiency and rotordynamic stability are paramount to subsea multiphase pump operation since, during the life of a well, the process fluid transitions from a pure liquid to a mixture of gas in the liquid to just gas. Circumferentially grooved seals commonly serve as balance pistons in pumps while also restricting secondary flow. Prior experimental results obtained with a grooved seal operating with a mixture of air and mineral oil show the seal rotordynamic force coefficients vary significantly with the gas volume fraction (GVF). This paper, complementing an exhaustive experimental program, presents a computational fluid dynamics (CFD) analysis to predict the leakage and dynamic force coefficients of a circumferentially grooved seal supplied with air in an oil mixture with a GVF varying from 0 to 0.7. The test seal has 14 grooves, an overall axial length of 43.6 mm, and radial clearance of 0.211 mm. The 127 mm diameter rotor spins at constant angular speed (Ω = 3500 rpm). The mixture enters the seal at a supply pressure (Pin) of 2.9 bar(a), and the seal exit pressure (Pout) is 1 bar(a). The CFD two-phase flow simulations utilize the Euler–Euler multiphase model to predict the mass flowrate and the pressure field as a function of the operating conditions. Using a multi-frequency shaft orbit motion method, the CFD simulations deliver the variations of reaction force on the rotor with respect to the excitation frequency. For a pure liquid condition (GVF = 0), both the CFD and experimental results produce constant stiffness, damping, and added mass coefficients. The experimental and CFD results demonstrate the seal rotordynamic force coefficients are quite sensitive to the GVF. When introducing a small amount of air into the oil (GVF = 0.1), the direct damping coefficient increases by approximately 10%. For operation with a mixture with inlet GVF > 0.1, the cross-coupled stiffness coefficients develop strong frequency-dependent characteristics. In contrast, the direct damping coefficient has a negligible variation with excitation frequency. The CFD predictions, as well as the experimental results, evidence that air injection in a liquid stream can significantly change the seal rotordynamic characteristics, and thus can affect the rotordynamic stability of a pump. An accurate CFD analysis provides engineers to design reliable grooved seals operating under two-phase flow conditions.

Multistage centrifugal pumps and compressors are among the most widely used pieces of rotating machinery in industry. A typical application demands the arrangement of several impellers or wheels mounted on a shaft that spins within a stationary case. Annular seals are the most common sealing devices used in this type of machinery. The annular seal design affects both (i) machinery performance in terms of energy conversion efficiency, and (ii) stability due to the interaction within the rotor and the stator through the fluid flow within the seals. Traditionally, the “bulk-flow” theory due to Hirs 1 has been used to estimate annular seals leakage and dynamic coefficients. To predict the flow behavior through the seal, this theory relies on empirical friction factor correlations. While leakage is well predicted, the dynamic coefficients are not. The discrepancy is attributed to the friction factor model. Several experiments have produced seal leakage data indicating that friction factor increases as the seal clearance is increased, contradicting predictions based on Moody’s pipe-friction model. A Computational Fluid Dynamics (CFD) commercial code was used to simulate flat-platechannel-flow experimental tests of water flowing within deliberately roughened surfaces, showing a directly proportional behavior of the friction factor versus the plate clearance. The higher friction factor characteristics of these deliberately roughened surfaces are governed by their ability to develop a high static pressure in the trailing face of each roughness cavity, while the wall shear stresses on the smooth land play a secondary role. In a certain Reynolds number range, the maximum friction factor observed in a specific roughness pattern size is independent of the actual clearance, in what we have referred to as the friction-factor-to-clearance indifference behavior. This phenomenon appears to be related to the roughness cavity size and its length-to-clearance ratio. NOMENCLATURE

The modern compressor operation is challenged by the liquid presence in wet gas operating conditions. The liquid phase may affect the compressor stability by partially flooding the internal annular gas seals and inducing subsynchronous vibration (SSV). To improve the annular seal behavior and increase the rotor stability, high-precision results of leakage flow rates and rotordynamic force coefficients are needed for annular gas seals in wet gas conditions. In order to better understand the leakage and rotordynamic characteristics of the annular gas seal in wet gas conditions, a 3D transient CFD-based perturbation method was proposed for computations of leakage flow rates and rotordynamic force coefficients of annular gas seals with liquid phase in main gas phase, based on inhomogeneous Eulerian-Eulerian multiphase flow model, mesh deformation technique, and the multifrequency rotor whirling orbit model. Numerical results of frequency-dependent rotordynamic force coefficients and leakage flow rates were presented and compared for three types of noncontact annular gas seals, which include a smooth plain annular seal (SPAS), a labyrinth (LABY) seal, and a fully partitioned pocket damper seal (FPDS). These three seals were designed to have the identical rotor diameter, sealing clearance, and axial length. The accuracy and the availability of the present transient CFD numerical method were demonstrated with the experiment data of leakage flow rates and frequency-dependent rotordynamic force coefficients of the smooth plain seal with four inlet liquid volume fractions (LVFs) of 0%, 2%, 5%, and 8%. Steady and transient numerical simulations were conducted at inlet air pressure of 62.1 bar, pressure ratio of 0.5, rotational speed of 15,000 rpm, and inlet preswirl ratio of 0.3 for four inlet LVFs varying from 0% to 8% and 14 subsynchronous and synchronous whirling frequencies up to 280 Hz. The numerical results show that the inlet liquid phase has a significant influence on the leakage and rotordynamic coefficients for all three types of annular gas seals. The mixture leakage flow rate increases with the increasing inlet LVF, combining the decreasing gas-phase and linearly increasing liquid-phase leakage flow rates. The smooth plain seal leaks the most gas phase and liquid phase, followed by the pocket damper seal (PDS) and then the labyrinth seal. Increasing inlet LVF significantly decreases the direct stiffness and slightly increases the effective damping of the smooth plain seal. The labyrinth seal possesses evident negative direct stiffness and shows a noticeable decreasing effective damping with the increasing inlet LVF at the subsynchronous frequency range. Increasing inlet LVF obviously increases all the force coefficients of the pocket damper seal including the positive effective damping. From a rotordynamic viewpoint, the FPDS possesses a better liquid tolerant capability and so is a better sealing scheme for the balance piston seals and center seals of the centrifugal compressor in wet gas operating condition.

A computational analysis for prediction of the static and dynamic forced performance of gas honeycomb seals at off-centered rotor conditions follows. The bulk-flow analysis, similar to the two-control volume flow model of Kleynhans and Childs (1997, “The Acoustic Influence of Cell Depth on the Rotordynamic Characteristics of Smooth-Rotor/Honeycomb-Stator Annular Gas Seals,” ASME J. Eng. Gas Turbines Power, 119, pp. 949–957), is brought without loss of generality into a single-control volume model, thus simplifying the computational process. The formulation accommodates the honeycomb effective cell depth, and existing software for annular pressure seals and is easily upgraded for damper seal analysis. An analytical perturbation method for derivation of zeroth- and first-order flow fields renders the seal equilibrium response and frequency-dependent dynamic force impedances, respectively. Numerical predictions for a centered straight-bore honeycomb gas seal shows good agreement with experimentally identified impedances, hence validating the model and confirming the paramount influence of excitation frequency on the rotordynamic force coefficients of honeycomb seals. The effect of rotor eccentricity on the static and dynamic forced response of a smooth annular seal and a honeycomb seal is evaluated for characteristic pressure differentials and rotor speeds. Leakage for the two seal types increases slightly as the rotor eccentricity increases. Rotor off-centering has a pronounced nonlinear effect on the predicted (and experimentally verified) dynamic force coefficients for smooth seals. However, in honeycomb gas seals, even large rotor center excursions do not sensibly affect the effective local film thickness, maintaining the flow azimuthal symmetry. The current model and predictions thus increase confidence in honeycomb seal design, operating performance, and reliability in actual applications.

A “credible” computational fluid dynamics (CFD) model has the potential to provide a meaningful evaluation of safety in medical devices. One major challenge in establishing “model credibility” is to determine the required degree of similarity between the model and experimental results for the model to be considered sufficiently validated. This study proposes a “threshold-based” validation approach that provides a well-defined acceptance criteria, which is a function of how close the simulation and experimental results are to the safety threshold, for establishing the model validity. The validation criteria developed following the threshold approach is not only a function of Comparison Error, E (which is the difference between experiments and simulations) but also takes in to account the risk to patient safety because of E. The method is applicable for scenarios in which a safety threshold can be clearly defined (e.g., the viscous shear-stress threshold for hemolysis in blood contacting devices). The applicability of the new validation approach was tested on the FDA nozzle geometry. The context of use (COU) was to evaluate if the instantaneous viscous shear stress in the nozzle geometry at Reynolds numbers (Re) of 3500 and 6500 was below the commonly accepted threshold for hemolysis. The CFD results (“S”) of velocity and viscous shear stress were compared with inter-laboratory experimental measurements (“D”). The uncertainties in the CFD and experimental results due to input parameter uncertainties were quantified following the ASME V&V 20 standard. The CFD models for both Re = 3500 and 6500 could not be sufficiently validated by performing a direct comparison between CFD and experimental results using the Student’s t-test. However, following the threshold-based approach, a Student’s t-test comparing |S-D| and |Threshold-S| showed that relative to the threshold, the CFD and experimental datasets for Re = 3500 were statistically similar and the model could be considered sufficiently validated for the COU. However, for Re = 6500, at certain locations where the shear stress is close the hemolysis threshold, the CFD model could not be considered sufficiently validated for the COU. Our analysis showed that the model could be sufficiently validated either by reducing the uncertainties in experiments, simulations, and the threshold or by increasing the sample size for the experiments and simulations. The threshold approach can be applied to all types of computational models and provides an objective way of determining model credibility and for evaluating medical devices.

Subsea pumps and compressors must withstand multiphase flows whose gas volume fraction (GVF) or liquid volume fraction (LVF) varies over a wide range. Gas or liquid content as a dispersed phase in the primary stream affects the leakage, drag torque, and dynamic forced performance of secondary flow components, namely seals, thus affecting the process efficiency and mechanical reliability of pumping/compressing systems, in particular during transient events with sudden changes in gas (or liquid) content. This paper, complementing a parallel experimental program, presents a computational fluid dynamics (CFD) analysis to predict the leakage, drag power, and dynamic force coefficients of a smooth surface, uniform clearance annular seal supplied with air in oil mixture whose inlet GVF varies discretely from 0.0 to 0.9, i.e., from a pure liquid stream to a nearly all-gas content mixture. The test seal has uniform radial clearance Cr = 0.203 mm, diameter D = 127 mm, and length L = 0.36 D. The tests were conducted with an inlet pressure/exit pressure ratio equal to 2.5 and a rotor surface speed of 23.3 m/s (3.5 krpm), similar to conditions in a pump neck wear ring seal. The CFD two-phase flow model, first to be anchored to test data, uses an Euler–Euler formulation and delivers information on the precise evolution of the GVF and the gas and liquid streams' velocity fields. Recreating the test data, the CFD seal mass leakage and drag power decrease steadily as the GVF increases. A multiple-frequency shaft whirl orbit method aids in the calculation of seal reaction force components, and from which dynamic force coefficients, frequency-dependent, follow. For operation with a pure liquid, the CFD results and test data produce a constant cross-coupled stiffness, damping, and added mass coefficients, while also verifying predictive formulas typical of a laminar flow. The injection of air in the oil stream, small or large in gas volume, immediately produces force coefficients that are frequency-dependent; in particular the direct dynamic stiffness which hardens with excitation frequency. The effect is most remarkable for small GVFs, as low as 0.2. The seal test direct damping and cross-coupled dynamic stiffness continuously drop with an increase in GVF. CFD predictions, along with results from a bulk-flow model (BFM), reproduce the test force coefficients with great fidelity. Incidentally, early engineering practice points out to air injection as a remedy to cure persistent (self-excited) vibration problems in vertical pumps, submersible and large size hydraulic. Presently, the model predictions, supported by the test data, demonstrate that even a small content of gas in the liquid stream significantly raises the seal direct stiffness, thus displacing the system critical speed away to safety. The sound speed of a gas in liquid mixture is a small fraction of those speeds for either the pure oil or the gas, hence amplifying the fluid compressibility that produces the stiffness hardening. The CFD model and a dedicated test rig, predictions and test data complementing each other, enable engineered seals for extreme applications.

Gas labyrinth seals: On the effect of clearance and operating conditions on wall friction factors – A CFD investigation

A transient bulk flow model with circular whirl motion for rotordynamic coefficients of annular seals

Aerodynamic characteristics of a guided rocket projectile are numerically simulated. Simulations are performed in a range of flight conditions using a commercial CFD software FLUENT, and variations of lift coefficients and drag coefficients with Mach numbers and angles of attack were demonstrated. The numerical results also indicate that the angle of canard deflection has significant influence on the flow field near tailfins.

Three-dimensional flow phenomena have been observed in a shock tube experiment for shock waves and vortices by using an interferometric CT (Computed Tomography) technique with a N2 pulse laser. A model with small duct, which has a pair of circular open ends, is introduced in a test section of diaphragmless shock tube, and can be rotated around its central axis to change the observation angle. The projection image of density distribution for each observation angle is obtained by using a fixed Mach-Zehnder interferometer. Three-dimensional density distribution is reconstructed from these projection images. The shock Mach number is 2.3 in nitrogen gas of 19.4kPa initial pressure at the exits of the open ends. The resultant 3-D density flow fields are illustrated by several imaging technique to clarify 3-D features of shock waves, vortices, and their mutual interactions. A computational fluid dynamics (CFD) simulation is also applied to the 3-D flow fields. The CFD results can represent density and another properties in flow fields, and these properties are useful for identifying the phenomena. The mutual validation between the experimental CT density results and these CFD results is discussed. Three-dimensional features of flow fields are investigated in detail by analyzing the experimental CT results with CFD results.

A fluid with a large swirl (circumferential) velocity entering an annular pressure seal influences the seal cross-coupled dynamic stiffness coefficients and hence it affects system stability. Typically comprising a large number of angled vanes around the seal circumference, a swirl brake (SB) is a mechanical element installed to reduce (even reverse) the swirl velocity entering an annular seal. SB design guidelines are not readily available and existing configurations appear to reproduce a single source. By using a computational fluid dynamics (CFD) model, the paper details a process to engineer a SB upstream of a sixteen-tooth labyrinth seal (LS) with tip clearance Cr = 0.203 mm. The process begins with a known nominal SB* geometry and considers variations in vane length (LV* = 3.25 mm) and width (WV* = 1.02 mm), and stagger angle (θ* = 0°). The vane number NV* = 72 and vane height HV* = 2.01 mm remain unchanged. The SB-LS operates with air supplied at pressure PS = 70 bar, a pressure ratio PR = exit pressure Pa / PS = 0.5, and rotor speed Ω = 10.2 krpm (surface speed ΩR = 61 m/s). Just before the SB the pre-swirl velocity ratio = average circumferential velocity U / shaft surface speed (ΩR) equals α = 0.5. For the given conditions, an increase in LV allows more space for the development of vortexes between two adjacent vanes. These are significant to the dissipation of fluid kinetic energy and thus control the reduction of α. A 42% increase in vane length (LV = 4.6 mm) produces a ∼ 43% drop in swirl ratio at the entrance of the LS (exit of the SB), from αE = 0.23 to 0.13. Based on the SB with LV = 4.6 mm, the stagger angle θ varies from 0° to 50°. The growth in angle amplifies a vortex at ∼ 70% of the vane height while it weakens a vortex at 30% of HV. For θ = 40°, the influence of the two vortexes on the flow produces the smallest swirl ratio at the LS entrance, αE = −0.03. For a SB with LV = 4.6 mm and θ = 40°, the vane width WV varies from 0.51 mm to 1.52 mm (± 50% of WV*). A reduction in WV provides more space for the strengthening of the vortex between adjacent vanes. Therefore, a SB with greater spacing of vanes also reduces the inlet circumferential velocity. For WV = 0.51 mm, αE further decreases to −0.07. Besides the design condition (α = 0.5), the engineered SB having LV = 4.6 mm, θ = 40° and WV = 0.51 mm effectively reduces the circumferential velocity at the LS entrance for other inlet pre-swirl ratios equaling α = 0 and 1.3. Rather than relying on extensive experiments, the CFD analysis proves effective to quickly engineer a best SB configuration from the quantification of performance while varying the SB geometry and inlet swirl condition.

Efficient design of an artificially roughened solar air heater with semi-cylindrical side walls: CFD and exergy analysis

Establishment and validation of a relationship model between nozzle experiments and CFD results based on convolutional neural network

Hole-pattern damper seal (textured stator with numerous circular-hole cavities and smooth rotor) is a typical annular damper seal that is gradually used in modern turbomachinery as a replacement of the conventional labyrinth seal to reduce the fluid leakage and stabilize the rotor-bearing system. It has been demonstrated that hole geometric design parameters (hole diameter and hole depth) have a decisive influence on the sealing capability and rotordynamic performance of hole-pattern damper seals, especially for the balance piston seal of high pressure turbomachinery where the seal sustains the quite high pressure difference and fluid density. In this paper, geometric configurations of hole-pattern damper seal with various hole diameter and depth were designed for the balance piston in a 14-MW supercritical CO2 turbine. To enhance the seal net damping capability at high inlet preswirl condition, a straight swirl brake also was designed and employed at seal entrance for each seal configuration. To better understand the sensitivity of geometric design parameters (hole diameter and depth) on the leakage and rotordynamic characteristics of the hole-pattern seals with inlet preswirl, a leakage computational model based on mesh deformation technology was proposed to predict the leakage flowrate with continuously varying hole depth, and a transient computational fluid dynamics (CFD)-based perturbation method based on the multiple-frequency elliptical-orbit rotor whirling model also was proposed to predict the frequency-dependent rotordynamic force coefficients. To take into account of real gas effect with high accuracy, a table look-up procedure based on the National Institute of Standards and Technology (NIST) database was implemented, using an in-house code, for the fluid properties of CO2 in both supercritical and subcritical conditions. The accuracy and availability of the present numerical methods and seal model were demonstrated based on the published experimental data of the leakage and force coefficients of hole-pattern damper seals with different hole diameters and depths. The leakage flow rates were predicted for hole-pattern seals with five hole diameters (D = 3.2 mm, 4.8 mm, 6.4 mm, 9.6 mm, and 12.8 mm) and continuously varying hole depth, the rotordynamic forces coefficients and response force vectors were presented for seals with the present five types of hole diameters and five hole depths (H = 0.8 mm, 1.6 mm, 3.2 mm, 4.8 mm, and 6.4 mm). Results show that the aspect ratio (Ar, the ratio of hole depth to diameter) is the key parameter affecting the seal leakage performance. Although the supercritical carbon dioxide (sCO2) hole pattern seal with smaller diameters (D = 3.2 mm, 4.8 mm) possesses the best sealing performance, especially at the range of Ar = 0.15–0.5, the leakage characteristics show a strong sensitivity to the aspect ratio: when Ar is less than 0.15 or more than 0.5, the leakage flowrate has a sharp increase (>14%). The hole depth and hole diameter possess a significant influence on the rotordynamic characteristics of sCO2 hole-pattern seals. For the present seal configurations in this paper, the seal with the shallower hole depth (H = 0.8 mm) or the larger hole diameter (D = 12.8 mm) has the best rotordynamic behavior, which possess the lower direct stiffness Kxx and larger effective damping Ceff.

Computational fluid dynamic (CFD) simulations in support of the SHARP-B2 (Slender Hypervelocity Aerothermodynamic Research Probes) program are presented. Pre-flight simulations of the aerothermal flight environment have been made to aid in the design of the flight hardware and instrumentation. Simulations of a critical flight qualification ground test performed in the 20 MW Panel Test Facility (PTF) arc jet, which is equipped with a semi-elliptical nozzle, have also been performed. The arc jet simulations were performed with the same CFD code that is used in the flight calculations. For both the flight and the arc jet simulations, the CFD results are used to provide surface heat transfer coefficients that serve as boundary conditions for an in-depth conduction thermal response code. By using the same CFD tool to compute the aerothermal environments for both the ground test and the flight test environment, useful comparisons are made regarding the traceability of the ground test environment to flight. Introduction The NASA Ames Research Center has been developing new Ultra High Temperature Ceramics (UHTC's) with the goal that these materials will enable sharp leading edges to be used for future space vehicles. Because of their unique thermo-structural properties, these materials are capable of operation at temperatures near 5100 °F without ablation. The materials have been developed and tested in ground-based arc jet facilities, and a flight test program designated SHARP (Slender Hypervelocity Aerothermodynamic Research Probes) has been initiated. The first flight demonstration, SHARP-B1, incorporated a UHTC nosetip mounted on a U.S. Air Force Mkl2A entry vehicle in collaboration with Sandia National Laboratory (SNL), and was successfully flown in May, 1997. The second flight test, SHARP-B2, which incorporated four instrumented UHTC strakes mounted on the side of the entry vehicle, was flown in September 2000. The goal of these flight tests is to assess the performance of the materials under entry conditions. The use of Computational Fluid Dynamic (CFD) simulations for the design of Thermal Protection Systems (TPS) has evolved to an extent that they have been integrated into the preliminary design process of Reusable Launch Vehicle (RLV) programs such as the X-33. Real-gas CFD simulations with finite-rate chemistry and proper boundary conditions for coupling with material thermal response codes are now routinely performed on high-end laboratory workstations. Much of the ground based testing of advanced TPS components is done in arc-heated test facilities such as those located in the Arc Jet Complex at the NASA Ames Research Center. These facilities are capable of simulating the high enthalpy flow environment experienced by entry vehicles for a broad range of test conditions and configurations. Semi-elliptical nozzles are available for the testing of flat panels in a high enthalpy boundary layer environment. CFD is • Aerospace Engineer, Reacting Flow Environments Branch, Member AIAA. t Senior Research Scientist, ELORET, Member AIAA. Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental Purposes. All other rights are reserved by the copyright owner. (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.