On the Influence of the Entrance Section on the Rotordynamic Performance of a Pump Seal With Uniform Clearance: A Sharp Edge Versus A Round Inlet

Secondary flows through annular seals in pumps must be minimized to improve their mechanical efficiency. Annular seals, in particular balance piston seals, also produce rotordynamic force coefficients, which easily control the placement of rotor critical speeds and determine system stability. A uniform clearance annular seal produces a direct (centering) static stiffness as a result of the sudden entrance pressure drop at its inlet plane when the fluid flow accelerates from an upstream (stagnant) flow region into a narrow film land. This so-called Lomakin effect equates the entrance pressure drop to the dynamic flow head through an empirical entrance pressure loss coefficient. Most seal designs regard the inlet as a sharp edge or square corner. In actuality, a customary manufacturing process could produce a rounded corner at the seal inlet. Furthermore, after a long period of operation, a sharp corner may wear out into a round section. Notice that to this date, bulk-flow model (BFM) analyses rely on a hitherto unknown entrance pressure coefficient to deliver accurate predictions for seal force coefficients. This paper establishes the ground to quantify the influence of an inlet round corner on the performance of a water lubricated seal reproducing a configuration tested by Marquette et al. (1997). The smooth surface seal has clearance Cr = 0.11 mm, length L = 35 mm, and diameter D = 76 mm (L/D = 0.46). The test case considers design operation at 10.2 krpm and 6.9 MPa pressure drop. Computational fluid dynamics (CFD) simulations apply to a seal with either a sharp edge or an inlet section with curvature rc varying from ¼Cr to 5Cr. Note the largest radius (rc) is just 1.6% of the overall seal length L. Going from a sharp edge inlet plane to one with a small curvature rc = ¼Cr produces a ∼20% decrease on the inlet pressure loss coefficient (ξ). A further reduction occurs with a larger circular corner; ξ drops from 0.43 to 0.17. That is, the entrance pressure loss will be lesser in a seal with a curved inlet. This can occur easily if the inlet edge wears due to solid particles eroding the seal inlet section. Further CFD simulations show that operating conditions in rotor speed and pressure drop do not affect the inlet loss coefficient, while the inlet circumferential swirl velocity does. In addition, further CFD results for a shorter (half) length seal produce a very similar entrance loss coefficient, whereas an enlarged (double) clearance seal leads to an increase in the entrance pressure loss parameter as the inlet section becomes less round. CFD predictions for most rotordynamic coefficients are within 10% relative to published test data, except for the direct damping coefficient C. For the seal with a rounded edge (rc = 5 Cr) at the inlet plane, both the direct stiffness K and direct damping C decrease about 10% compared against the coefficients for the seal with a sharp inlet edge. The other force coefficients, namely cross-coupled stiffness and added mass, are unaffected by the inlet edge geometry. The same result holds for seal leakage, as expected. A BFM incorporates the CFD derived entrance pressure loss coefficients and produces rotordynamic coefficients for the same operating conditions. The CFD and BFM predictions are in good agreement, though there is still ∼10% discrepancy for the direct stiffnesses delivered by the two methods. In the end, the analysis of the CFD results quantifies the pressure loss coefficient as a function of the inlet geometry for ready use in engineering BFM tools.

On the Influence of the Entrance Section on the Rotordynamic Performance of a Pump Seal With Uniform Clearance: A Sharp Edge vs. a Round Inlet

Secondary flows thru annular seals in pumps must be minimized to improve their mechanical efficiency. Annular seals, in particular balance piston seals, also produce rotordynamic force coefficients which easily control the placement of rotor critical speeds and determine system stability. A uniform clearance annular seal produces a direct (centering) static stiffness as a result of the sudden entrance pressure drop at its inlet plane when the fluid flow accelerates from an upstream (stagnant) flow region into a narrow film land. This so called Lomakin effect equates the entrance pressure drop to the dynamic flow head through an empirical entrance pressure loss coefficient. Most seal designs regard the inlet as a sharp edge or square corner. In actuality, a customary manufacturing process could produce a rounded corner at the seal inlet. Furthermore, after a long period of operation, a sharp corner may wear out into a round section. Notice that to this date, bulk flow model (BFM) analyses rely on a hitherto unknown entrance pressure coefficient to deliver accurate predictions for seal force coefficients. This paper establishes the ground to quantify the influence of an inlet round corner on the performance of a water lubricated seal reproducing a configuration tested by Marquette et al. (1997). The smooth surface seal has clearance Cr = 0.11 mm, length L = 35 mm, and diameter D = 76 mm (L/D = 0.46). The test case considers design operation at 10.2 krpm and 6.9 MPa pressure drop. Computational fluid dynamics (CFD) simulations apply to a seal with either a sharp edge or an inlet section with curvature rc varying from ¼Cr to 5Cr. Note the largest radius (rc) is just 1.6% of the overall seal length L. Going from a sharp edge inlet plane to one with a small curvature rc = ¼Cr produces a ∼20% decrease on the inlet pressure loss coefficient (ξ). A further reduction occurs with a larger circular corner; ξ drops from 0.43 to 0.17. That is, the entrance pressure loss will be lesser in a seal with a curved inlet. This can occur easily if the inlet edge wears due to solid particles eroding the seal inlet section. Further CFD simulations show that operating conditions in rotor speed and pressure drop do not affect the inlet loss coefficient, while the inlet circumferential swirl velocity does. In addition, further CFD results for a shorter (half) length seal produce a very similar entrance loss coefficient, whereas an enlarged (double) clearance seal leads to an increase in the entrance pressure loss parameter as the inlet section becomes less round. CFD predictions for most rotordynamic coefficients are within 10% relative to published test data, except for the direct damping coefficient C. For the seal with a rounded edge (rc = 5 Cr) at the inlet plane, both the direct stiffness K and direct damping C decrease about 10% compared against the coefficients for the seal with a sharp inlet edge. The other force coefficients, namely cross-coupled stiffness and added mass, are unaffected by the inlet edge geometry. The same result holds for seal leakage, as expected. A BFM incorporates the CFD derived entrance pressure loss coefficients and produces rotordynamic coefficients for the same operating conditions. The CFD and BFM predictions are in good agreement, though there is still ∼10% discrepancy for the direct stiffnesses delivered by the two methods. In the end, the analysis of the CFD results quantifies the pressure loss coefficient as a function of the inlet geometry for ready use in engineering BFM tools.

Entrance pressure instability of LLDPE and its composites

The relationship between entrance pressure fluctuation and perturbation of the extrudates was elaborated experimentally.

The Influence of Inlet Pressure Control on Separation Performance of Multi-Product Cyclones

This paper is devoted and intended to solve the problems in determining the precise separation efficiency and accurate prediction for the solid yield of multi-product cyclones based on existing experimental data. The influence of inlet pressure control on separation performance of multi-product cyclones is investigated. Hydrocyclone separation performance is influenced by many factors such as the liquid level of agitating vessel and the entrance pressure. The liquid level can also be controlled through the entrance pressure control. The mathematical model of multi-product cyclone system is a high-order complex model and it is difficult to determine the specific expressions. The paper adopts a special optimal fuzzy PI_PID control strategy performed by Programmable Logic Controller system to enable inlet pressure control. By the force of contrast with experiment and analysis for many performance indexes, the effectiveness and applicability of the control approach are demonstrated. The research provides a method for control of high-order complex system of hydrocyclone separation.

Numerical Simulation of the Hydrodynamic Cavitation of the Impinging Streams Mixer

The impinging streams mixer is a new type micromixer. The cavitation phenomenon occurring in the mixers with T-shaped impinging streams (TS), conical impinging streams (CIS), vortex streams(VS) were investigated, respectively. The distribution of flow field in the mixer was simulated and calculated by commercial software Fluent 6.2.1. The results showed that under the same working conditions, a more obvious hydrodynamic cavitation may occur in the CIS type impinging stream than that in the CIS type or the VS type, and the vortex flow lead to an extension of the material residence time in the mixer. The distribution of turbulent kinetic energy and gas holdup were obtained by numerical simulating hydrodynamic cavitation under different entrance pressure conditions. It is showed that when the outlet pressure keeps a constant value, hydrodynamic cavitation can be enhanced by increasing the entrance pressure. The above research can be contributed to the producing of biodiesel and the solving of the key technical problem of oil and alcohol heterogeneous mixing.

Analysis of Y Type Branch Pipe Exhaust Ventilation Flow Characteristics

In order to study the internal gas flow of Y type branch pipes in the exhaust ventilation conditions, the branch pipe is simulated by using FLUENT software. Combined with experimental results, comparatively analyze exhaust ventilation pressure, velocity and vortex flow of the branch pipe. The results show that simulation and experimental data consistent overall trend, the difference is less than 8%, the main entrance pressure of the branch pipeline decreases with the width of the leakage increasing, leakage width of 0 mm, 1 mm, 2 mm cases, there is vortex tube, and valve and the main ventilation pipe case gas exchange occurs when no leakage, this study provides a theoretical and practical basis for further analysis of branch pipe exhaust ventilation.

Size Design of Capillary and Barrel of Multi-Function and All-Electric Rheometer

Multi-function and all-electric rheometer (MAR) was designed by the authors to study the nonlinear viscoelasticity of polymer melts at high shear rate. It is important to design suitable size of capillary and barrel because it is the calculation basis for some other important parts and determines the shear rate range of MAR. Considering the shear rate range, the entrance pressure correction and the wall slip correction, the length and diameter of capillary and barrel of MAR were designed through particular analysis and precise calculation.

The Frequency-Domain Analysis of the Rheological Data Acquired with Multi-Function and All-Electric Rheometer

The key parts of multi-function and all-electric rheometer (MAR) designed by the authors were introduced. The data processing method based on frequency-domain analysis were established. Intrinsic vibration displacement is defined to eliminate the effect of steady velocity displacement and extract the useful information of vibration displacement. The actual frequency, amplitude and phase of the superimposed vibration displacement and the entrance pressure were obtained by the frequency-domain analysis of the intrinsic vibration displacement and the entrance pressure. The control precision of the superimposed vibration displacement frequency and amplitude of MAR proved to be high. The direct current component of entrance pressure can be seen as the mean entrance pressure which stands for the flow resistance. The study of mean entrance pressure is useful in discovering the energy consumption mechanism of the polymer processing introduced vibration energy. Loss angle can be calculate according to the phase of entrance pressure and superimposed vibration displacement. The higher order harmonic of the entrance pressure can be used to characterize the nonlinear viscoelasticity of polymer melts. The factors which depend on the shear rate and influence the viscoelasitic properties can be studied by test the loss angle based on MAR.