Two Dimensional Oscillatory Flow Analysis in the Pulse Tubes

2008 ◽  
Author(s):  
M. H. Saidi ◽  
M. Taheri ◽  
R. Jahanbakhshi ◽  
A. Jafarian ◽  
S. K. Hannani
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Oscillatory Flow ◽  
Present Model ◽  
Flow Analysis ◽  
Harmonic Approximation ◽  
Ideal Gas ◽  
Approximation Technique ◽  
Pulse Tube ◽  
Two Dimensional

Recently a great attention has been given to the oscillatory flow modeling in the pulse tube cryocoolers. In this paper multi dimensioning effects of the fluid flow in the pulse tube are investigated. A complete system of governing equations is solved to report the flow field, friction coefficient and Nusselt number in the pulse tube. Harmonic approximation technique is employed to derive an analytical solution. In this respect, mass, momentum and energy balance equations as well as the equation of state for ideal gas are transformed by implementing the harmonic approximation technique. The present model is able to predict the behavior of the two dimensional compressible oscillatory flow in the tube section of the regenerative cryocoolers. Based on the proposed analytical model, friction coefficient and complex Nusselt number is reported.

scholarly journals The effect of variable magnetic field on heat transfer and flow analysis of unsteady squeezing nanofluid flow between parallel plates using Galerkin method

2017 ◽  
Vol 21 (5) ◽  
pp. 2057-2067 ◽  
Author(s):  
Mohammad Rahimi-Gorji ◽  
Oveis Pourmehran ◽  
Mofid Gorji-Bandpy ◽  
Davood Ganji
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Galerkin Method ◽  
Skin Friction ◽  
Flow Analysis ◽  
Skin Friction Coefficient ◽  
Variable Magnetic Field ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Squeeze Number

This paper presents a thermal and flow analysis of an unsteady squeezing nanofluid flow and heat transfer using nanofluid based on Brinkman model in presence of variable magnetic field. Galerkin method is used to solve the non-linear differential equations governing the problem. Squeezing flow between parallel plates is very applicable in the many industries and it means that one or both of the parallel plates have vacillation. The effects of active parameters such as the Hartman number, squeeze number, and heat source parameter are discussed. Results for temperature distribution and velocity profile, Nusselt number, and skin friction coefficient by Galerkin method are presented. As can be seen in results, the values of Nusselt number and skin friction coefficient for CuO is better than Al2O3. Also, according to figures, as nanofluid volume fraction increases, Nusselt number increases and skin friction coefficient decreases, increase in the Hartman number results in an increase in velocity and temperature profiles and an increase in squeeze number can be associated with the decrease in the velocity. <br><br><font color="red"><b> This article has been corrected. Link to the correction <u><a href="http://dx.doi.org/10.2298/TSCI171204246E">10.2298/TSCI171204246E</a><u></b></font>

scholarly journals Uncertainties Analysis on the Prediction of Flow and Heat Transfer of Liquid Sodium with CFD Technology

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhanwei Liu ◽  
Xinyu Li ◽  
Tenglong Cong ◽  
Rui Zhang ◽  
Lingyun Zheng ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Liquid Sodium ◽  
Heat Transfer Characteristics ◽  
Backward Facing Step ◽  
Heating Wall ◽  
Transfer Characteristics ◽  
Cfd Models ◽  
Flow And Heat Transfer

The prediction of flow and heat transfer characteristics of liquid sodium with CFD technology is of significant importance for the design and safety analysis of sodium-cooled fast reactor. The accuracies and uncertainties of the CFD models should be evaluated to improve the confidence of the numerical results. In this work, the uncertainties from the turbulent model, boundary conditions, and physical properties for the flow and heat transfer of liquid sodium were evaluated against the experimental data. The results of uncertainty quantization show that the maximum uncertainties of the Nusselt number and friction coefficient occurred in the transition zone from the inlet to the fully developed region in the circular tube, while they occurred near the reattachment point in the backward-facing step. Furthermore, in backward-facing step flow, the maximum uncertainty of temperature migrated from the heating wall to the geometric center of the channel, while the maximum uncertainty of velocity occurred near the vortex zone. The results of sensitivity analysis illustrate that the Nusselt number was negatively correlated with the thermal conductivity and turbulent Prandtl number, while the friction coefficient was positively correlated with the density and Von Karman constant. This work can be a reference to evaluate the accuracy of the standard k-ε model in predicting the flow and heat transfer characteristics of liquid sodium.

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

Grid-Free Vortex Methods for Natural Convection in Two-Dimensional Domains

2012 ◽  
Author(s):  
Issam Lakkis
Keyword(s):  
Natural Convection ◽  
Nonlinear Diffusion ◽  
Reacting Flows ◽  
Ideal Gas ◽  
Two Dimensional ◽  
Vortex Methods ◽  
Free Vortex ◽  
Low Mach Number ◽  
Buoyancy Driven Flows ◽  
Vorticity Generation

Vortex methods for simulating natural convection of an ideal gas in unbounded two-dimensional domains are presented. In particular, the redistribution method for diffusion is extended to enable simulation of nonlinear diffusion of an ideal gas in isobaric conditions encountered in unbounded low-Mach number flows. We also address the problem of handling source terms in grid-free vortex methods and propose a fast, accurate, and physically motivated method for solving the associated inverse problems. Examples include generation of baroclinic vorticity in non-reacting buoyancy driven flows, and in addition, generation of internal energy and species in buoyant reacting flows. Accuracy and speed of the proposed algorithms for nonlinear diffusion and vorticity generation are investigated separately. Simulations of natural convection of a “thermal patch” for Grashof number ranging from to 1562.5 to 25000 are presented.

Analysis of Hiemenz flow of Reiner-Rivlin fluid over a stretching/shrinking sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Golam Mortuja Sarkar ◽  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Nusselt Number ◽  
Stability Analysis ◽  
Friction Coefficient ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Content Type ◽  
Hiemenz Flow ◽  
Self Similar ◽  
The Stability

Purpose This paper aims to theoretically and numerically investigate the steady two-dimensional (2D) Hiemenz flow with heat transfer of Reiner-Rivlin fluid over a linearly stretching/shrinking sheet. Design/methodology/approach The Navier–Stokes equations are transformed into self-similar equations using appropriate similarity transformations and then solved numerically by using shooting technique. A simple but effective mathematical analysis has been used to prove the existence of a solution for stretching case (λ> 0). Moreover, an attempt has been laid to carry the asymptotic solution behavior for large stretching. The obtained asymptotic solutions are compared with direct numerical solutions, and the comparison is quite remarkable. Findings It is observed that the self-similar equations exhibit dual solutions within the range [λc, −1] of shrinking parameter λ, where λc is the turning point from where the dual solutions bifurcate. Unique solution is found for all stretching case (λ > 0). It is noticed that the effects of cross-viscous parameter L and shrinking parameter λ on velocity and thermal fields show opposite character in the dual solution branches. Thus, a linear temporal stability analysis is performed to determine the basic feasible solution. The stability analysis is based on the sign of the smallest eigenvalue, where positive or negative sign leading to a stable or unstable solution. The stability analysis reveals that the first solution is stable that describes the main flow. Increase in cross-viscous parameter L resulting in a significant increment in skin friction coefficient, local Nusselt number and dual solutions domain. Originality/value This work’s originality is to examine the combined effects of cross-viscous parameter and stretching/shrinking parameter on skin friction coefficient, local Nusselt number, velocity and temperature profiles of Hiemenz flow over a stretching/shrinking sheet. Although many studies on viscous fluid and nanofluid have been investigated in this field, there are still limited discoveries on non-Newtonian fluids. The obtained results can be used as a benchmark for future studies of higher-grade non-Newtonian flows with several physical aspects. All the generated results are claimed to be novel and have not been published elsewhere.

scholarly journals Two Dimensional Flow Analysis of a Laboratory Centrifugal Pump

1990 ◽  
Author(s):  
S. M. Miner ◽  
R. D. Flack ◽  
P. E. Allaire
Keyword(s):  
Velocity Field ◽  
Stagnation Point ◽  
Centrifugal Pump ◽  
Flow Rate ◽  
Flow Analysis ◽  
Tangential Component ◽  
Design Flow ◽  
Experimental Results ◽  
Two Dimensional ◽  
Flow Angle

Two dimensional potential flow was used to determine the velocity field within a laboratory centrifugal pump. In particular, the finite element technique was used to model the impeller and volute simultaneously. The rotation of the impeller within the volute was simulated by using steady state solutions with the impeller in 10 different angular orientations. This allowed the interaction between the impeller and the volute to develop naturally as a result of the solution. The results for the complete pump model showed that there are circumferential asymmetries in the velocity field, even at the design flow rate. Differences in the relative velocity components were as large as 0.12 m/sec for the radial component and 0.38 m/sec for the tangential component, at the impeller exit. The magnitude of these variations was roughly 25% of the magnitude of the average radial and tangential velocities at the impeller exit. These asymmetries were even more pronounced at off design flow rates. The velocity field was also used to determine the location of the tongue stagnation point and to calculate the slip within the impeller. The stagnation point moved from the discharge side of the tongue to the impeller side of the tongue, as the flow rate increased from below design flow to above design flow. At design flow, values of slip ranged from 0.96 to 0.71, from impeller inlet to impeller exit. For all three types of data (velocity profiles, stagnation point location, and slip factor) comparison was made to laser velocimeter data, taken for the same pump. At the design flow, the computational and experimental results agreed to within 17% for the velocity magnitude, and 2° for the flow angle. The stagnation point locations coincided for the computational and experimental results, and the values for slip agreed to within 10%.

Thermo-Elasto-Hydro-Dynamic Modeling of Hydrostatic Seals in Reactor Coolant Pumps

2005 ◽  
Author(s):  
Erwan Galenne ◽  
Isabelle Pierre-Danos
Keyword(s):  
Pressure Drop ◽  
Present Model ◽  
Operating Mode ◽  
Hysteretic Behavior ◽  
Two Dimensional ◽  
Critical Component ◽  
Dimensional Approach ◽  
Reactor Coolant ◽  
Energy Company ◽  
Injection Temperature

The French energy company EDF has experienced in the last years some problems in managing reactor coolant pumps (RCP) seals in operation. That’s why a thermo-elasto-hydrodynamical model of the seal has been developed. The present model is a steady two-dimensional approach so as to characterize the normal operating mode of the seal. Numerical results are successfully compared to experimental results of leak-flow rate. The influence of pressure drop and injection temperature is described. The influence of the conicity of the faceplates is underlined. The friction is introduced in the model in order to reproduce the hysteretic behavior of the seal. The development of this model leads to a better knowledge of the behavior of a critical component.

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