scholarly journals Analysis of Flow Evolution and Thermal Instabilities in the Near-Nozzle Region of a Free Plane Laminar Jet

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Hector Barrios-Piña ◽  
Hermilo Ramírez-León ◽  
Carlos Couder-Castañeda
Keyword(s):  
Numerical Simulations ◽  
Temperature Difference ◽  
Stokes Equations ◽  
Boussinesq Approximation ◽  
Stability Diagram ◽  
Ideal Gas ◽  
Unsteady State ◽  
Laminar Jet ◽  
Jet Stability ◽  
Free Plane

This work focuses on the evolution of a free plane laminar jet in the near-nozzle region. The jet is buoyant because it is driven by a continuous addition of both buoyancy and momentum at the source. Buoyancy is given by a temperature difference between the jet and the environment. To study the jet evolution, numerical simulations were performed for two Richardson numbers: the one corresponding to a temperature difference slightly near the validity of the Boussinesq approximation and the other one corresponding to a higher temperature difference. For this purpose, a time dependent numerical model is used to solve the fully dimensional Navier-Stokes equations. Density variations are given by the ideal gas law and flow properties as dynamic viscosity and thermal conductivity are considered nonconstant. Particular attention was paid to the implementation of the boundary conditions to ensure jet stability and flow rates control. The numerical simulations were also reproduced by using the Boussinesq approximation to find out more about its pertinence for this kind of flows. Finally, a stability diagram is also obtained to identify the onset of the unsteady state in the near-nozzle region by varying control parameters of momentum and buoyancy. It is found that, at the onset of the unsteady state, momentum effects decrease almost linearly when buoyancy effects increase.

Numerical simulation of natural convection using unsteady compressible Navier-stokes equations

2017 ◽  
Vol 27 (11) ◽  
pp. 2508-2527 ◽  
Author(s):  
Mahmoud M. El-Gendi ◽  
Abdelraheem M. Aly
Keyword(s):  
Natural Convection ◽  
Temperature Difference ◽  
Stokes Equations ◽  
Calculated Data ◽  
Boussinesq Approximation ◽  
Density Variation ◽  
Navier Stokes ◽  
Large Temperature ◽  
Present Calculation ◽  
Content Type

Purpose Boussinesq approximation is widely used in solving natural convection problems, but it has severe practical limitations. Using Boussinesq approximation, the temperature difference should be less than 28.6 K. The purpose of this study is to get rid of Boussinesq approximation and simulates the natural convection problems using an unsteady compressible Navier-Stokes solver. The gravity force is included in the source term. Three temperature differences are used namely 20 K, 700 K and 2000 K. Design/methodology/approach The calculations are carried out on the square and sinusoidal cavities. The results of low temperature difference have good agreement with the experimental and previous calculated data. It is found that, the high temperature difference has a significant effect on the density. Findings Due to mass conservation, the density variation affects the velocity distribution and its symmetry. On the other hand, the density variation has a negligible effect on the temperature distribution. Originality/value The present calculation method has no limitations but its convergence is slow. The current study can be used in fluid flow simulations for nuclear power applications in natural convection flows subjected to large temperature differences.

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.

scholarly journals Compressible integral representation of rotational and axisymmetric rocket flow

2016 ◽  
Vol 809 ◽  
pp. 213-239 ◽  
Author(s):  
M. Akiki ◽  
J. Majdalani
Keyword(s):  
Numerical Simulations ◽  
Closed Form ◽  
Mass Flux ◽  
Mathematical Formulation ◽  
Circular Cross Section ◽  
Ideal Gas ◽  
Injection Rate ◽  
Dimensional Solution ◽  
Abel Transformation ◽  
Injection Speed

This work focuses on the development of a semi-analytical model that is appropriate for the rotational, steady, inviscid, and compressible motion of an ideal gas, which is accelerated uniformly along the length of a right-cylindrical rocket chamber. By overcoming some of the difficulties encountered in previous work on the subject, the present analysis leads to an improved mathematical formulation, which enables us to retrieve an exact solution for the pressure field. Considering a slender porous chamber of circular cross-section, the method that we follow reduces the problem’s mass, momentum, energy, ideal gas, and isentropic relations to a single integral equation that is amenable to a direct numerical evaluation. Then, using an Abel transformation, exact closed-form representations of the pressure distribution are obtained for particular values of the specific heat ratio. Throughout this effort, Saint-Robert’s power law is used to link the pressure to the mass injection rate at the wall. This allows us to compare the results associated with the axisymmetric chamber configuration to two closed-form analytical solutions developed under either one- or two-dimensional, isentropic flow conditions. The comparison is carried out assuming, first, a uniformly distributed mass flux and, second, a constant radial injection speed along the simulated propellant grain. Our amended formulation is consequently shown to agree with a one-dimensional solution obtained for the case of uniform wall mass flux, as well as numerical simulations and asymptotic approximations for a constant wall injection speed. The numerical simulations include three particular models: a strictly inviscid solver, which closely agrees with the present formulation, and both $k$–$\unicode[STIX]{x1D714}$ and Spalart–Allmaras computations.

scholarly journals Computational Analysis of the Performance Characteristics of a Supercritical CO2 Centrifugal Compressor

Computation ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 54 ◽  
Author(s):  
Senthil Raman ◽  
Heuy Kim
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
National Laboratory ◽  
Sandia National Laboratory ◽  
Ideal Gas ◽  
Operating Conditions ◽  
Tip Clearance ◽  
Performance Characteristics ◽  
Supercritical Regime ◽  
Vaned Diffuser

A centrifugal compressor working with supercritical CO 2 (S-CO 2 ) has several advantages over other supercritical and conventional compressors. S-CO 2 is as dense as the liquid CO 2 and becomes difficult to compress. Thus, during the operation, the S-CO 2 centrifugal compressor requires lesser compression work than the gaseous CO 2 . The performance of S-CO 2 compressors is highly varying with tip clearance and vanes in the diffuser. To improve the performance of the S-CO 2 centrifugal compressor, knowledge about the influence of individual components on the performance characteristics is necessary. This present study considers an S-CO 2 compressor designed with traditional engineering design tools based on ideal gas behaviour and tested by SANDIA national laboratory. Three-dimensional, steady, viscous flow through the S-CO 2 compressor was analysed with computational fluid dynamics solver based on the finite volume method. Navier-Stokes equations are solved with K- ω (SST) turbulence model at operating conditions in the supercritical regime. Performance of the impeller, the main component of the centrifugal compressor is compared with the impeller with vaneless diffuser and vaned diffuser configurations. The flow characteristics of the shrouded impeller are also studied to analyse the tip-leakage effect.

scholarly journals Analytical and Numerical Feasibility Analysis of a Contra-Rotary Ramjet Engine

Energies ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 163
Author(s):  
Tomasz Laube ◽  
Janusz Piechna
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Analytical Data ◽  
Combustion Process ◽  
Flow Characteristics ◽  
Combustion Model ◽  
Similar Data ◽  
High Rotational Speed ◽  
Jet Engine ◽  
Ramjet Engine

A new idea for a contra-rotary ramjet engine is presented. To define the theoretical limits of the non-typical, contra-rotary ramjet engine configuration, its analytical model was developed. The results obtained from that model and the analytical results were compared with those received from numerical simulations. The main weakness of existing rotary ramjet engine projects is the very high rotational speed of the rotor required for achieving supersonic inlet flow. In this paper, a new idea for a contra-rotary ramjet engine (CORRE) is presented and analyzed. This paper presents the results of analytical analysis and numerical simulations of a jet engine system with two rotors rotating in opposite directions. Contra-rotating rotors generate a supersonic air velocity at the inlet to the compressor at two times slower rotor’s speed. To determine the flow characteristics, combustion process, and engine efficiency of the double-rotor engine, a numerical solution of the average Navier-Stokes equations was used with the k-eps turbulence model and the non-premixed combustion model. The results of numerical simulations of flow and the combustion process inside the contra-rotary jet engine achieving a shockwave compression are shown and compared with similar data for a single-rotor engine design and analytical data. This paper presents only the calculation results of the flow processes and the combustion process, indicating the advantages of the proposed double-rotor design. The results of the numerical analysis were presented on the contours and diagrams of the pressure and flow velocity, temperature distribution, and mass fraction of the fuel.

Effects of Buoyancy on Laminar Flow in Curved Elliptic Ducts

1992 ◽  
Vol 114 (4) ◽  
pp. 936-943 ◽  
Author(s):  
Z. F. Dong ◽  
M. A. Ebadian
Keyword(s):  
Laminar Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Uniform Heat Flux ◽  
Published Data ◽  
Circular Duct ◽  
Uniform Wall Temperature ◽  
Wide Range

This paper numerically investigates the effects of buoyancy on fully developed laminar flow in a curved duct with an elliptic cross section. The flow of Newtonian fluids is assumed steady in terms of Boussinesq approximation. The curved elliptic duct is subjected to thermal boundary conditions of axially uniform heat flux and peripherally uniform wall temperature. The numerically generated boundary-fitted coordinate system is applied to discretize the solution domain of the elliptic duct, and the Navier-Stokes equations and the energy equation, including the curvature ratio, are solved by use of the control volume-based finite difference method. The solution covers a wide range of curvature ratios, and Dean and Grashof numbers. The results presented are displayed graphically and in tabular form to illustrate the buoyancy effect. It is further shown that buoyancy acts to increase both the Nusselt number and the friction factor and changes the distribution of the velocity and the temperature. The results for the curved circular duct with and without buoyancy are compared with the data available in the open literature for all cases. Also compared with the published data are the results of laminar flow in a curved elliptic duct, and very good agreement is obtained.

Flow induced by jets and plumes

1981 ◽  
Vol 108 ◽  
pp. 55-65 ◽  
Author(s):  
W. Schneider
Keyword(s):  
Stokes Equations ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Slip Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laminar Jet ◽  
Order Of Magnitude ◽  
Valid Solution ◽  
Solid Walls

The order of magnitude of the flow velocity due to the entrainment into an axisymmetric, laminar or turbulent jet and an axisymmetric laminar plume, respectively, indicates that viscosity and non-slip of the fluid at solid walls are essential effects even for large Reynolds numbers of the jet or plume. An exact similarity solution of the Navier-Stokes equations is determined such that both the non-slip condition at circular-conical walls (including a plane wall) and the entrainment condition at the jet (or plume) axis are satisfied. A uniformly valid solution for large Reynolds numbers, describing the flow in the laminar jet region as well as in the outer region, is also given. Comparisons show that neither potential flow theory (Taylor 1958) nor viscous flow theories that disregard the non-slip condition (Squire 1952; Morgan 1956) provide correct results if the flow is bounded by solid walls.

scholarly journals The linear instability of the stratified plane Couette flow

2018 ◽  
Vol 853 ◽  
pp. 205-234 ◽  
Author(s):  
Giulio Facchini ◽  
Benjamin Favier ◽  
Patrice Le Gal ◽  
Meng Wang ◽  
Michael Le Bars
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Couette Flow ◽  
Vertical Direction ◽  
Stability Diagram ◽  
Linear Instability ◽  
Plane Couette Flow ◽  
Horizontal Shear ◽  
The Stability

We present the stability analysis of a plane Couette flow which is stably stratified in the vertical direction orthogonal to the horizontal shear. Interest in such a flow comes from geophysical and astrophysical applications where background shear and vertical stable stratification commonly coexist. We perform the linear stability analysis of the flow in a domain which is periodic in the streamwise and vertical directions and confined in the cross-stream direction. The stability diagram is constructed as a function of the Reynolds number $Re$ and the Froude number $Fr$, which compares the importance of shear and stratification. We find that the flow becomes unstable when shear and stratification are of the same order (i.e. $Fr\sim 1$) and above a moderate value of the Reynolds number $Re\gtrsim 700$. The instability results from a wave resonance mechanism already known in the context of channel flows – for instance, unstratified plane Couette flow in the shallow-water approximation. The result is confirmed by fully nonlinear direct numerical simulations and, to the best of our knowledge, constitutes the first evidence of linear instability in a vertically stratified plane Couette flow. We also report the study of a laboratory flow generated by a transparent belt entrained by two vertical cylinders and immersed in a tank filled with salty water, linearly stratified in density. We observe the emergence of a robust spatio-temporal pattern close to the threshold values of $Fr$ and $Re$ indicated by linear analysis, and explore the accessible part of the stability diagram. With the support of numerical simulations we conclude that the observed pattern is a signature of the same instability predicted by the linear theory, although slightly modified due to streamwise confinement.

Modeling Of The Alloying Substances Distribution In The Melt During Pulsed Induction Heating Of The Substrate

2017 ◽  
Vol 12 (2) ◽  
pp. 111-118
Author(s):  
Vladimir Popov
Keyword(s):  
Induction Heating ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Empirical Formulas ◽  
Metal Solidification ◽  
Navier Stokes Equations ◽  
High Frequency Electromagnetic Field ◽  
Melting And Solidification

Under study is the applicability of the high-frequency electromagnetic field impulse for metal heating and melting with a view to its subsequent alloying. The processes of heating, phase transition, heat and mass transfer in the molten metal, solidification of the melt are considered with the aid the proposed mathematical model. The substrate surface is covered with a layer of alloying substances. The distribution of the electromagnetic energy in the metal is described by empirical formulas. Melting and solidification of the metal is considered at the Stephan’s approximation. The flow in the liquid is described by the Navier – Stokes equations in the Boussinesq approximation. According to the results of numerical experiments, the flow structure in the melt and distribution of the alloying substances was evaluated versus the characteristics of induction heating

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