On the Non-Uniqueness of the Parallel-Flow Approximation

1992 ◽  
pp. 344-355 ◽  
Author(s):  
C. David Pruett ◽  
Lian L. Ng ◽  
Gordon Erlebacher
Keyword(s):  
Parallel Flow ◽  
Flow Approximation

Mean flow refraction effects on sound radiated from localized sources in a jet

1998 ◽  
Vol 370 ◽  
pp. 149-174 ◽  
Author(s):  
CHRISTOPHER K. W. TAM ◽  
LAURENT AURIAULT
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Acoustic Waves ◽  
Flow Direction ◽  
Jet Flow ◽  
Parallel Flow ◽  
Mean Flow ◽  
Flow Approximation ◽  
Radiated Sound ◽  
Localized Sources

It is well-known that sound generated by localized sources embedded in a jet undergoes refraction as the acoustic waves propagate through the jet mean flow. For isothermal or hot jets, the effect of refraction causes the deflection of the radiated sound waves away from the jet flow direction. This gives rise to a cone of silence around the jet axis where there is a significant reduction in the radiated sound intensity. In this work, the mean flow refraction problem is investigated through the use of the reciprocity principle. Instead of the direct source Green's function, the adjoint Green's function with the source and observation points interchanged is used to quantify the effect of mean flow on sound radiation. One advantage of the adjoint Green's function is that the Green's functions for all the source locations in the jet radiating to a given direction in the far field can be obtained in a single calculation. This provides great savings in computational effort. Another advantage of the adjoint Green's function is that there is no singularity in the jet flow so that the problem can be solved numerically with axial as well as radial mean flow gradients included in a fairly straightforward manner. Extensive numerical computations have been carried out for realistic jet flow profiles with and without exercising the locally parallel flow approximation. It is concluded that the locally parallel flow approximation is valid as long as the direction of radiation is outside the cone of silence.

Thermosolutal bifurcation phenomena in porous enclosures subject to vertical temperature and concentration gradients

1999 ◽  
Vol 395 ◽  
pp. 61-87 ◽  
Author(s):  
M. MAMOU ◽  
P. VASSEUR
Keyword(s):  
Perturbation Theory ◽  
Travelling Waves ◽  
Neumann Boundary ◽  
Lewis Number ◽  
Parallel Flow ◽  
Nonlinear Perturbation ◽  
Concentration Gradients ◽  
Bifurcation Phenomena ◽  
Flow Approximation ◽  
Vertical Walls

The Darcy model with the Boussinesq approximations is used to study double-diffusive instability in a horizontal rectangular porous enclosure subject to two sources of buoyancy. The two vertical walls of the cavity are impermeable and adiabatic while Dirichlet or Neumann boundary conditions on temperature and solute are imposed on the horizontal walls. The onset and development of convection are first investigated using the linear and nonlinear perturbation theories. Depending on the governing parameters of the problem, four different regimes are found to exist, namely the stable diffusive, the subcritical convective, the oscillatory and the augmenting direct regimes. The governing parameters are the thermal Rayleigh number, RT, buoyancy ratio, N, Lewis number, Le, normalized porosity of the porous medium, ε, aspect ratio of the enclosure, A, and the thermal and solutal boundary condition type, κ, applied on the horizontal walls. On the basis of the nonlinear perturbation theory and the parallel flow approximation (for slender or shallow enclosures), analytical solutions are derived to predict the flow behaviour. A finite element numerical method is introduced to solve the full governing equations. The results indicate that steady convection can arise at Rayleigh numbers below the supercritical value, indicating the development of subcritical flows. At the vicinity of the threshold of supercritical convection the nonlinear perturbation theory and the parallel flow approximation results are found to agree well with the numerical solution. In the overstable regime, the existence of multiple solutions, for a given set of the governing parameters, is demonstrated. Also, numerical results indicate the possible occurrence of travelling waves in an infinite horizontal enclosure.

scholarly journals Linear and Nonlinear Stability Analyses of Double-Diffusive Convection in a Vertical Brinkman Porous Enclosure under Soret and Dufour Effects

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 292
Author(s):  
Amel Bouachir ◽  
Mahmoud Mamou ◽  
Redha Rebhi ◽  
Smail Benissaad
Keyword(s):  
Porous Layer ◽  
Convective Flow ◽  
Parallel Flow ◽  
Double Diffusive Convection ◽  
Soret And Dufour Effects ◽  
Convective Flows ◽  
Diffusive Convection ◽  
Flow Approximation ◽  
Convective State ◽  
Double Diffusive

Analytical and numerical investigations were performed to study the influence of the Soret and Dufour effects on double-diffusive convection in a vertical porous layer filled with a binary mixture and subject to horizontal thermal and solute gradients. In particular, the study was focused on the effect of Soret and Dufour diffusion on bifurcation types from the rest state toward steady convective state, and then toward oscillatory convective state. The Brinkman-extended Darcy model and the Boussinesq approximation were employed to model the convective flow within the porous layer. Following past laboratory experiments, the investigations dealt with the particular situation where the solutal and thermal buoyancy forces were equal but acting in opposite direction to favor the possible occurrence of the rest state condition. For this situation, the onset of convection could be either supercritical or subcritical and occurred at given thresholds and following various bifurcation routes. The analytical investigation was based on the parallel flow approximation, which was valid only for a tall porous layer. A numerical linear stability analysis of the diffusive and convective states was performed on the basis of the finite element method. The thresholds of supercritical, RTCsup, and overstable, RTCover, convection were computed. In addition, the stability of the established convective flow, predicted by the parallel flow approximation, was studied numerically to predict the onset of Hopf’s bifurcation, RTCHopf, which marked the transition point from steady toward unsteady convective flows; a route towards the chaos. To support the analytical analyses of the convective flows and the numerical stability methodology and results, nonlinear numerical solutions of the full governing equations were obtained using a second-order finite difference method. Overall, the Soret and Dufour effects were seen to affect significantly the thresholds of stationary, overstable and oscillatory convection. The Hopf bifurcation was marked by secondary convective flows consisting of superposed vertical layers of opposite traveling waves. A good agreement was found between the predictions of the parallel flow approximation, the numerical solution and the linear stability results.

Linear Stability of Jet Flows

1977 ◽  
Vol 44 (3) ◽  
pp. 378-384 ◽  
Author(s):  
A. K. Bajaj ◽  
V. K. Garg
Keyword(s):  
Stability Theory ◽  
Outer Region ◽  
Parallel Flow ◽  
Jet Flows ◽  
Complex Eigenvalue ◽  
Spatial Stability ◽  
Laminar Jets ◽  
Flow Approximation ◽  
The Stability ◽  
Asymptotic Forms

A theoretical investigation into the linear, spatial stability of plane laminar jets is presented. The three cases studied are: 1. Inviscid stability of Sato’s velocity profile. 2. Viscous stability of the Bickley’s jet using parallel-flow stability theory. 3. Viscous stability of the Bickley’s jet using a theory modified to account for the inflow terms. The integration of stability equations is started from the outer region of the jet toward the jet axis using the solution of the asymptotic forms of the governing equations. An eigenvalue search technique is employed to find the number of eigenvalues and their approximate location in a closed region of the complex eigenvalue plane. The accurate eigenvalues are obtained using secant method. The inviscid spatial stability theory is found to give results that are in better agreement with Sato’s experimental results than those obtained by him after transformation of the temporal theory results. For the viscous case the critical Reynolds number found by using the theory accounting for inflow is in better agreement with the experimental value than that given by the parallel-flow theory, implying thereby that the parallel-flow approximation for a jet is erroneous for the stability analysis.

Parametric Study of Photovoltaic Thermal Solar Collector Using An Improved Parallel Flow

2020 ◽  
Vol 2 (1) ◽  
pp. 19-24
Author(s):  
Sakhr Mohammed Sultan ◽  
Chih Ping Tso ◽  
Ervina Efzan Mohd Noor ◽  
Fadhel Mustafa Ibrahim ◽  
Saqaff Ahmed Alkaff
Keyword(s):  
Thermal Conductivity ◽  
Energy Balance ◽  
Parametric Study ◽  
Solar Collector ◽  
Parallel Flow ◽  
Operating Conditions ◽  
Balance Equations ◽  
Conductivity Type ◽  
Pv Module ◽  
Sunny Weather

Photovoltaic Thermal Solar Collector (PVT) is a hybrid technology used to produce electricity and heat simultaneously. Current enhancements in PVT are to increase the electrical and thermal efficiencies. Many PVT factors such as type of absorber, thermal conductivity, type of PV module and operating conditions are important parameters that can control the PVT performance. In this paper, an analytical model, using energy balance equations, is studied for PVT with an improved parallel flow absorber. The performance is calculated for a typical sunny weather in Malaysia. It was found that the maximum electrical and thermal efficiencies are 12.9 % and 62.6 %, respectively. The maximum outlet water temperature is 59 oC.

Two-Phase Refrigerant Distribution in a Parallel-Flow Heat Exchanger

2010 ◽  
Vol 17 (1) ◽  
pp. 59-75 ◽  
Author(s):  
Nae-Hyun Kim ◽  
D. Y. Kim
Keyword(s):  
Heat Exchanger ◽  
Parallel Flow ◽  
Two Phase ◽  
Flow Heat
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