An analytically predictive model for moderately rarefied gas flow

2012 ◽  
Vol 698 ◽  
pp. 406-422 ◽  
Author(s):  
Thomas Veltzke ◽  
Jorg Thöming
Keyword(s):  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Knudsen Diffusion ◽  
Convective Transport ◽  
Surface Topology ◽  
Fickian Diffusion ◽  
Navier Stokes ◽  
Navier Stokes Equations

AbstractIn microducts deviation from continuum flow behaviour of a gas increases with rarefaction. When using Navier–Stokes equations to calculate a flow under slightly and moderately rarefied conditions, slip boundary conditions are used which in turn refer to the tangential momentum accommodation coefficient (TMAC). Here we demonstrate that, in the so-called slip and transition regime, the flow in microducts can be reliably described by a consistently non-empirical model without considering the TMAC. We obtain this equation by superposition of convective transport and Fickian diffusion using two-dimensional solutions of Navier–Stokes equations and a description for the Knudsen diffusion coefficient as derived from kinetic theory respectively. For a wide variety of measurement series found in the literature the calculation predicts the data accurately. Surprisingly only size of the duct, temperature, gas properties and inlet and outlet pressure are necessary to calculate the resulting mass flow by means of a single algebraic equation. From this, and taking the discrepancies of the TMAC concerning surface roughness and nature of the gases into account, we could conclude that neither the diffusive proportions nor the total mass flow rates are influenced by surface topology and chemistry at Knudsen numbers below unity. Compared to the tube geometry, the model slightly underestimates the flow rate in rectangular channels when rarefaction increases. Likewise, the dimensionless mass flow rate and the diffusive proportion of the total flow are distinctly higher in a tube. Thus the cross-sectional geometry has a significant influence on the transport mechanisms under rarefied conditions.

scholarly journals Development of Hybrid Airlift-Jet Pump with Its Performance Analysis

2018 ◽  
Vol 8 (9) ◽  
pp. 1413 ◽  
Author(s):  
Dan Yao ◽  
Kwongi Lee ◽  
Minho Ha ◽  
Cheolung Cheong ◽  
Inhiug Lee
Keyword(s):  
Boundary Conditions ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Jet Pump ◽  
Two Phase

A new pump, called the hybrid airlift-jet pump, is developed by reinforcing the advantages and minimizing the demerits of airlift and jet pumps. First, a basic design of the hybrid airlift-jet pump is schematically presented. Subsequently, its performance characteristics are numerically investigated by varying the operating conditions of the airlift and jet parts in the hybrid pump. The compressible unsteady Reynolds-averaged Navier-Stokes equations, combined with the homogeneous mixture model for multiphase flow, are used as the governing equations for the two-phase flow in the hybrid pump. The pressure-based methods combined with the Pressure-Implicit with Splitting of Operators (PISO) algorithm are used as the computational fluid dynamics techniques. The validity of the present numerical methods is confirmed by comparing the predicted mass flow rate with the measured ones. In total, 18 simulation cases that are designed to represent the various operating conditions of the hybrid pump are investigated: eight of these cases belong to the operating conditions of only the jet part with different air and water inlet boundary conditions, and the remaining ten cases belong to the operating conditions of both the airlift and jet parts with different air and water inlet boundary conditions. The mass flow rate and the efficiency are compared for each case. For further investigation into the detailed flow characteristics, the pressure and velocity distributions of the mixture in a primary pipe are compared. Furthermore, a periodic fluctuation of the water flow in the mass flow rate is found and analyzed. Our results show that the performance of the jet or airlift pump can be enhanced by combining the operating principles of two pumps into the hybrid airlift-jet pump, newly proposed in the present study.

scholarly journals Performance investigation of a volute porous tongue of a turbocharger turbine

2020 ◽  
Vol 40 (1) ◽  
pp. 59-66
Author(s):  
Abderrahmane Chachoua ◽  
Mohamed Kamal Hamidou ◽  
Mohammed Hamel
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Gas Turbines ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Recirculation Flow ◽  
Recirculating Flow ◽  
Show Evidence ◽  
The Right

The design for better performance of the spiral housing volute used commonly in radial and mixed inflow gas turbines is of prime importance as it affects the machine stage at both design and off design conditions. The tongue of the scroll divides the flow into two streams, and represents a severe source of disturbances, in terms of thermodynamic parameter uniformity, maximum kinetic energy, the right angle of attack to the rotor and minimum losses. Besides, the volute suffers an undesirable effect due to the recirculating mass flow rate in near bottom vicinity of the tongue. The present project is an attempt to design a tongue fitted with cylindrical holes traversing normal to the stream wise direction, where on account of the large pressure difference between the top and the bottom sides of the tongue will force the recirculating flow to go through the rotor inlet. This possibility with its limitations has not yet been explored. A numerical simulation is performed which might provide our suitable objectives. To achieve this goal the ANSYS code is used to build the geometry, generate the mesh, and to simulate the flow by solving numerically the averaged Navier Stokes equations. Apparently, the numerical results show evidence of favorable impact in using porous tongue. The realization of a contact between the main and recirculation flow by drilled holes on the tongue surface leads to a flow field uniformity, a reduction in the magnitude of the loss coefficient, and a 20 % reduction in the recirculating mass flow rate.

Oscillatory forcing of flow through porous media. Part 1. Steady flow

2002 ◽  
Vol 465 ◽  
pp. 213-235 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Media ◽  
Flow Rate ◽  
Stokes Equations ◽  
Nonlinear Flow ◽  
Navier Stokes ◽  
Full Time ◽  
Inertial Effects ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Oscillatory forcing of a porous medium may have a dramatic effect on the mean flow rate produced by a steady applied pressure gradient. The oscillatory forcing may excite nonlinear inertial effects leading to either enhancement or retardation of the mean flow. Here, in Part 1, we consider the effects of non-zero inertial forces on steady flows in porous media, and investigate the changes in the flow character arising from changes in both the strength of the inertial terms and the geometry of the medium. The steady-state Navier–Stokes equations are solved via a Galerkin finite element method to determine the velocity fields for simple two-dimensional models of porous media. Two geometric models are considered based on constricted channels and periodic arrays of circular cylinders. For both geometries, we observe solution multiplicity yielding both symmetric and asymmetric flow patterns. For the cylinder arrays, we demonstrate that inertial effects lead to anisotropy in the effective permeability, with the direction of minimum resistance dependent on the solid volume fraction. We identify nonlinear flow phenomena which might be exploited by oscillatory forcing to yield a net increase in the mean flow rate. In Part 2, we take up the subject of unsteady flows governed by the full time-dependent Navier–Stokes equations.

Steady streaming in a turbulent oscillating boundary layer

2007 ◽  
Vol 571 ◽  
pp. 265-280 ◽  
Author(s):  
PIETRO SCANDURA
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Stokes Equations ◽  
Infinite Plate ◽  
Harmonic Component ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Steady Streaming ◽  
Time Average

The turbulent flow generated by an oscillating pressure gradient close to an infinite plate is studied by means of numerical simulations of the Navier–Stokes equations to analyse the characteristics of the steady streaming generated within the boundary layer. When the pressure gradient that drives the flow is given by a single harmonic component, the time average over a cycle of the flow rate in the boundary layer takes both positive and negative values and the steady streaming computed by averaging the flow over n cycles tends to zero as n tends to infinity. On the other hand, when the pressure gradient is given by the sum of two harmonic components, with angular frequencies ω1 and ω2 = 2ω1, the time average over a cycle of the flow rate does not change sign. In this case steady streaming is generated within the boundary layer and it persists in the irrotational region. It is shown both theoretically and numerically that in spite of the presence of steady streaming, the time average over n cycles of the hydrodynamic force, acting per unit area of the plate, vanishes as n tends to infinity.

Simulation-Based Analysis of 3D Flow Inside a Micropump With Passive Valves

2007 ◽  
Author(s):  
A. F. Tabak ◽  
A. Solak ◽  
E. Y. Erdem ◽  
C. Akcan ◽  
S. Yesilyurt
Keyword(s):  
Flow Rate ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Driving Frequency ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
New Developments ◽  
Arbitrary Lagrangian Eulerian Method ◽  
Simulation Based

It is expected that chemical, biological and environmental applications of microdevices will increase with new developments in micromachining techniques. In this work, a micropump design that utilizes passive valves and an actuated diaphragm is presented. The flow rate is controlled by the deflection and the frequency of the diaphragm’s displacement. Passive valves are used for directing the flow. Poiseuille flow analogy is used to generate the equivalent pressure drop and flow rate via modifying the viscosity in the valve-channel in order to replace the variation of the channel width due to valve movement. Overall flow in the micropump is governed by three-dimensional time-dependent Navier Stokes equations. Deformation of the domain due to moving boundaries that coincide with the diaphragm motion is handled with the arbitrary Lagrangian-Eulerian method. Flow rate, hydraulic power and the efficiency of the micropump are obtained with respect to driving frequency and displacement of the diaphragm.

Modeling the Effect of Stability Bleed on Back-Pressure in Mixed-Compression Supersonic Inlets

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Lv Yongzhao ◽  
Li Qiushi ◽  
Li Shaobin
Keyword(s):  
Mach Number ◽  
Flow Rate ◽  
Stokes Equations ◽  
Functional Relation ◽  
Back Pressure ◽  
Normal Shock ◽  
Navier Stokes ◽  
Correction Coefficient ◽  
Navier Stokes Equations ◽  
Plenum Pressure

To stabilize the terminal normal shock on high-static pressure at outlet, called back-pressure pout, stability bleed slots are used in the throat of mixed-compression supersonic inlets. In this paper, a model for the functional relation between the bleed flow rate mbl and back-pressure pout is established based on a bleed flow rate model (BFRM) in order to study the effect of stability bleed on the back-pressure in mixed-compression supersonic inlets. Given the inlet flow parameters Min, pin*, and Tin*, the plenum pressure ppl at slots' outlet, the terminal normal shock position xs in this model, the bleed flow rate mbl, Mach number M¯out, and back-pressure pout were derived one by one from the basic laws of conservation. To study the effect of plenum pressure ppl on subsonic flow of the divergent section behind the terminal normal shock, a correction coefficient κ is introduced to modify the Mach number M¯out. Furthermore, numerical simulations based on Reynolds-Averaged Navier–Stokes equations were performed to analyze the functional relation between the bleed flow rate mbl and back-pressure pout. Computational fluid dynamics (CFD) results show that the present model agrees with the data.

Rarefied Gas Flow Analysis of a Suborbital Shuttle With the Academic CFD Code Galatea

2017 ◽  
Author(s):  
Angelos G. Klothakis ◽  
Georgios N. Lygidakis ◽  
Ioannis K. Nikolos
Keyword(s):  
Gas Flow ◽  
Microelectromechanical Systems ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Flow Analysis ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rarefied Gas Flows ◽  
Wide Range

During the past decade considerable efforts have been exerted for the simulation of rarefied gas flows in a wide range of applications, like the flow over suborbital vehicles, in microelectromechanical systems, etc. Such flows appear to be significantly different from those at the continuum regime, making the Navier-Stokes equations to fail without further amendment. In this study an in-house academic CFD solver, named Galatea, is modified appropriately to account for rarefied gases. The no-slip condition on solid walls is no longer valid, hence, velocity slip and temperature jump boundary conditions are applied instead. Additionally, a second-order accurate slip model has been incorporated, namely, this of Beskok and Karniadakis, increasing the accuracy in the same area but avoiding simultaneously the numerical difficulties, entailed by the computation of the second derivative of slip velocity when complex geometries and unstructured grids are coupled. The proposed solver is validated against rarefied laminar flow over a suborbital shuttle, designed by the Azim’UTBM team. The obtained results are compared with those extracted with the parallel open-source kernel SPARTA, which is based on the DSMC method. A satisfactory agreement is reported between the two methodologies, demonstrating the potential of the modified solver to simulate effectively such flows.

The effects of surface roughness on the flow in multiple connected fractures

2022 ◽  
Author(s):  
Pouria Aghajannezhad ◽  
Mathieu Sellier
Keyword(s):  
Surface Roughness ◽  
Hydraulic Resistance ◽  
Flow Rate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Roughness Coefficient ◽  
Computationally Efficient ◽  
Navier Stokes Equations ◽  
Discrete Fracture Networks ◽  
The Impact

Abstract We present a novel computationally efficient approach for investigating the effect of surface roughness on the fluid flow in discrete fracture networks at low Reynolds number. The effect of parallel and series fracture arrangements on the flow rate and hydraulic resistance was studied numerically by patching Hele-Shaw (HS) cells to represent the network. In this analysis, the impact of surface roughness was studied in different arrangements of the network. For this aim, four models with different sequences of fracture connections were studied. The validity of the models was assessed by comparing the results with solutions of the full Navier-Stokes equations (NSE). The approximate hydraulic resistance and flow rate calculated by the HS method were found to be in good agreement with the NSE (less than 7% deviation). Results suggest a quadratic relationship between the network hydraulic resistance and the joint roughness coefficient (JRC). Notably, an increase in surface roughness caused a growth in hydraulic resistance and a fall in flow rate. Further insight was provided by drawing an analogy between resistors in electrical circuits and fractures in networks.

Entrainment in Free Jets

2005 ◽  
Author(s):  
Pasquale M. Sforza
Keyword(s):  
Mass Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Inertial Force ◽  
Axial Direction ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Free Jet ◽  
Plane Normal ◽  
Mass Entrainment

The mass flow passing through a plane normal to the mainstream direction of a free jet is the sum of the mass flow of the jet and that of the fluid entrained from surrounding ambient into which it issues. Manipulation of the instantaneous Navier-Stokes equations and the continuity equation yields an integro-differential equation for the instantaneous mass flow in the flow field. This equation is reduced to a form that suggests that jet entrainment may be viewed as a one-dimensional unsteady diffusion process with an integral source term arising from the gradient of forces in the axial direction of flow which are dependent, in general, on z and t. The small difference in the integrals of the net axial inertial force acting on the fluid in the volume defined by the limits of integration is balanced by an axial force arising from the viscous normal stress that is associated with axial rate of mass entrainment. Furthermore, it suggests that the kinematic viscosity of the fluid is the appropriate diffusion parameter. This formulation is used to assess the nature of the entrainment process in steady three-dimensional jets and to propose means for managing that process.

On Leakage Issues of Sucker Rod Pumping Systems

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Sheldon Wang ◽  
Lynn Rowlan ◽  
Mahmoud Elsharafi ◽  
Mansur A. Ermila ◽  
Tomas Grejtak ◽  
...  
Keyword(s):  
Flow Rate ◽  
Pressure Difference ◽  
Stokes Equations ◽  
Production Systems ◽  
Measurement Techniques ◽  
Navier Stokes ◽  
Outer Diameter ◽  
Navier Stokes Equations ◽  
Operation Conditions ◽  
Sucker Rod

The issues of leakage with respect to the clearance between the pump plunger outer diameter and the pump barrel inner diameter and other operation conditions have been revisited in this paper. Both Poiseuille flow rate due to the pressure difference and Couette flow rate due to the plunger motion have been considered. The purpose of this study is to better understand the nature of the leakage with respect to pressure difference, eccentricity, and motion related to the plunger of typical sucker rod pump systems. More specifically, based on the newly derived relaxation time scales for transient solutions of the governing Navier–Stokes equations, the quasi-static nature of relevant measurement techniques is confirmed for the current production systems. This key observation is also demonstrated with a computational model using the experimentally measured pressure difference and the plunger movement.

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