Numerical Simulation of an Acoustically Driven Resonator With Internal Thin Parallel Plates

2007 ◽  
Author(s):  
Yiqiang Lin ◽  
Bakhtier Farouk
Keyword(s):  
Acoustic Waves ◽  
High Performance ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Heat Engine ◽  
Temperature Fields ◽  
Thin Plates ◽  
Parallel Plates ◽  
Left Wall ◽  
Thermoacoustic Refrigerators

Heat transfer and flow characteristics in a two-dimensional resonator with inside thin plates due to acoustic excitations are investigated numerically. The effect of the presence of the internal thin plates in the resonators is then studied. Such parallel plates (stacks) have been used in acoustic resonators for developing thermoacoustic refrigerators and thermoacoustic engines. A fully compressible form of the Navier-Stokes equations is considered for the numerical model and an explicit time-marching algorithm is used to track the acoustic waves and energy flux. Numerical solutions are obtained by employing a highly accurate flux corrected transport (FCT) algorithm. In the present model, the acoustic waves are induced by vibrations of the left wall, and the right wall is stationary. By neglecting the effect of side walls, the top and bottom boundary conditions are assumed to be symmetric. No simplifying assumption is made regarding the existence of the acoustic field. The interaction of acoustic standing waves with the internal parallel plates produces a temperature difference between the two ends which can be used for refrigeration or to do work (as a heat engine). The temperature differences are found to be significantly dependent on the location, length and gap of the internal plates. The model developed can be used for the analysis of flow and temperature fields driven by acoustic transducers, as well as in the design of high-performance resonators for thermoacoustic refrigerators and engines.

Heat Transfer Enhancement by Acoustic Streaming in an Enclosure

2005 ◽  
Vol 127 (12) ◽  
pp. 1313-1321 ◽  
Author(s):  
Murat K. Aktas ◽  
Bakhtier Farouk ◽  
Yiqiang Lin
Keyword(s):  
Heat Transfer ◽  
Acoustic Waves ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Standing Waves ◽  
Side Wall ◽  
Temperature Fields ◽  
Vertical Side ◽  
Acoustic Standing Wave

Thermal convection in a differentially heated shallow enclosure due to acoustic excitations induced by the vibration of a vertical side wall is investigated numerically. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to track the acoustic waves. Numerical solutions are obtained by employing a highly accurate flux corrected transport algorithm. The frequency of the wall vibration is chosen such that an acoustic standing wave forms in the enclosure. The interaction of the acoustic standing waves and the fluid properties trigger steady secondary streaming flows in the enclosure. Simulations were also carried out for “off-design” vibration frequency where no standing waves were formed. The effects of steady second order acoustic streaming structures are found to be more significant than the main oscillatory flow field on the heat transfer rates. The model developed can be used for the analysis of flow and temperature fields driven by acoustic transducers and in the design of high performance resonators for acoustic compressors.

COMPARATIVE STUDY OF THERMAL FLOWS WITH DIFFERENT FINITE VOLUME AND LATTICE BOLTZMANN SCHEMES

2004 ◽  
Vol 15 (02) ◽  
pp. 307-319 ◽  
Author(s):  
AHMAD AL-ZOUBI ◽  
GUNTHER BRENNER
Keyword(s):  
Heat Transfer ◽  
Comparative Study ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Hybrid Approach ◽  
Navier Stokes ◽  
Steady Flows ◽  
Parallel Plates

In the present paper, a comparative study of numerical solutions for steady flows with heat transfer based on the finite volume method (FVM) and the relatively new lattice Boltzmann method (LBM) is presented. In the last years, the LB methods have challenged the classical FV methods to solve the Navier–Stokes equations and have proven to be superior in accuracy and efficiency for certain applications. Most of these studies were related to the transport of mass and momentum. In the meantime, significant effort has been invested in the application of the LBM to simulate flows including heat transfer. The studies in the present paper are the analysis of performance and accuracy aspects of LBM applied to the prediction of these flows. For a fully developed laminar flow between parallel plates, analytical solutions for the heat transfer in fully developed thermal boundary layers are available and may be compared with the respective numerical results. Finally, a hybrid approach is proposed to circumvent numerical problems of the thermal LB methods.

Natural convection in an enclosure having a vertical sidewall with time-varying temperature

1996 ◽  
Vol 329 ◽  
pp. 65-88 ◽  
Author(s):  
Ho Sang Kwak ◽  
Jae Min Hyun
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Time Varying ◽  
Vertical Sidewall ◽  
Boussinesq Fluid

A numerical study is performed for time-varying natural convection of an incompressible Boussinesq fluid in a sidewall-heated square cavity. The temperature at the cold sidewall Tc is constant, but at the hot sidewall a time-varying temperature condition is prescribed, $ T_H = \overline{T_H} + \Delta T^{\prime} \sin ft $. Comprehensive numerical solutions are found for the time-dependent Navier–Stokes equations. The numerical results are analysed in detail to show the existence of resonance, which is characterized by maximal amplification of the fluctuations of heat transfer in the interior. Plots of the dependence of the amplification of heat transfer fluctuations on the non-dimensional forcing frequency ω are presented. The failure of Kazmierczak & Chinoda (1992) to identify resonance is shown to be attributable to the limitations of the parameter values they used. The present results illustrate that resonance becomes more distinctive for large Ra and Pr ∼ 0(1). The physical mechanism of resonance is delineated by examining the evolution of oscillating components of flow and temperature fields. Specific comparisons are conducted for the resonance frequency ωr between the present results and several other previous predictions based on the scaling arguments.

Cavity flows driven by buoyancy and shear

1972 ◽  
Vol 51 (2) ◽  
pp. 221-231 ◽  
Author(s):  
K. Torrance ◽  
R. Davis ◽  
K. Eike ◽  
P. Gill ◽  
D. Gutman ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Cavity Flows ◽  
Navier Stokes Equations ◽  
Moving Wall ◽  
Aspect Ratios ◽  
Range Of Values

Fluid motion driven by the combined effects of a moving wall and natura convection is examined for rectangular cavities with heightlwidth ratios of ½, 1 and 2. The Reynolds number and Prandtl number are held fixed at Re = 100 and Pr = 1; the Grashof number is varied over the range of values Gr = 0, ±104, ±106. Flow and temperature fields obtained from numerical solutions of the Navier-Stokes equations reveal a marked influence of buoyancy for the larger aspect ratios when Gr = ±106 and the dominance of buoyancy for all aspect ratios when Gr = ± 106. Results are compared with earlier work where possible and some observations are offered on the convergence of the numerical solutions.

New boundary conditions in the transition régime

1968 ◽  
Vol 2 (3) ◽  
pp. 293-310 ◽  
Author(s):  
Carlo Cercignani ◽  
Gino Tironi
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Slip Flow ◽  
Navier Stokes ◽  
Main Body ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Flow Heat

Starting from the Boltzmann equation, new boundary conditions are derived to be matched with the Navier—Stokes equations, that are supposed to hold in the main body of a gas. The idea upon which this method is based goes back to Maxwell and Langmuir. Since the distribution function is supposed to be completely determined by the Navier—Stokes equations, this new set of boundary conditions extends in some sense the validity of the macroscopic equations to the transition and free molecular régimes. In fact, it is shown that the free molecular and slip flow régimes are correctly described by this method; the latter is also supposed to give a reasonable approximation for the complete range of Knudsen numbers. The new procedure is applied to different problems such as plane Couette flow, plane and cylindrical Poiseuile flow, heat transfer between parallel plates and concentric cylinders. Results are obtained and compared with the exact numerical solutions for the above-mentioned problems.

Numerical Study of an Evaporating Meniscus on a Moving Heated Surface

Volume 3 ◽  
2004 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Satish G. Kandlikar
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Numerical Study ◽  
Heated Surface ◽  
Nucleate Boiling ◽  
Two Dimensions ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Wall Heat Transfer ◽  
Parallel Plates

The present study is performed to numerically analyze an evaporating meniscus on a moving heated surface. This phenomenon is similar to the one observed at the base of a vapor bubble during nucleate boiling. The complete Navier-Stokes equations along with continuity and energy equations are solved. The liquid vapor interface is captured using the level set technique. A column of liquid is placed between two parallel plates with an inlet for water at the top to feed the meniscus. The location of water inlet at the top is kept fixed and the bottom wall is imparted with a velocity. Calculations are done in two-dimensions with a fixed distance between the plates. The main objective is to study the velocity and temperature fields inside the meniscus and calculate the wall heat transfer. The results show that the wall velocity creates a circulation near the meniscus base causing increased wall heat transfer as compared to a stationary meniscus. The local wall heat transfer is found to vary significantly along the meniscus base, the highest being near the advancing contact line.

scholarly journals Features of heat and mass exchange in laminar flows of micro and nanofluids in tubes and channels

2018 ◽  
pp. 62-67
Author(s):  
N. Kizilova ◽  
Ye. Tkachenko
Keyword(s):  
Momentum Transfer ◽  
High Efficiency ◽  
Stokes Equations ◽  
Heat Removal ◽  
Laminar Flows ◽  
Heat Fluxes ◽  
Thermal Dissipation ◽  
Temperature Fields ◽  
Parallel Plates ◽  
Heat And Mass Exchange

In recent years, high efficiency of using suspensions of nanoparticles for cooling of the operating systems compared to a homogeneous liquid has been shown, and the parameters of suspensions effective for various specific devices have been selected in experiments. A brief review of the relevant experimental data, as well as mathematical models of the flow of micro- and nanofluids, based on the incompressible Navier-Stokes equations with boundary conditions accounting for tangential momentum transfer of the particles and temperature jump due to diffuse reflection at rough walls, are presented. For the case of a laminar flow between infinite parallel plates with constant heat fluxes through the plates, an analytical solution is obtained for the velocity and temperature fields. Numerical calculations showed that with an increase in the momentum transfer coefficients at the plates, the flow accelerates significantly, which contributes to an increase in volumetric flow with the same pressure drop across the channel due to a decrease in the shear stress at the wall. Correspondingly, the heat transfer through the plates and the heat removal with the fluid flow increase. Based on the obtained analytical relationships, it is possible to select the parameters of the plate surfaces in such a way as to optimize the system, for example, to reduce the energy loss due to viscous and thermal dissipation or to obtain uniform temperature distributions in the liquid with asymmetric heat flows through the plates.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

scholarly journals Revisiting Surface-Subsurface Exchange at Intertidal Zone with a Coupled 2D Hydrodynamic and 3D Variably-Saturated Groundwater Model

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 902
Author(s):  
Zhi Li ◽  
Ben R. Hodges
Keyword(s):  
Intertidal Zone ◽  
Coastal Wetlands ◽  
High Performance ◽  
Stokes Equations ◽  
Wave Model ◽  
Surface Flow ◽  
Richards Equation ◽  
Navier Stokes ◽  
Dynamic Surface ◽  
Flow Equations

A new high-performance numerical model (Frehg) is developed to simulate water flow in shallow coastal wetlands. Frehg solves the 2D depth-integrated, hydrostatic, Navier–Stokes equations (i.e., shallow-water equations) in the surface domain and the 3D variably-saturated Richards equation in the subsurface domain. The two domains are asynchronously coupled to model surface-subsurface exchange. The Frehg model is applied to evaluate model sensitivity to a variety of simplifications that are commonly adopted for shallow wetland models, especially the use of the diffusive wave approximation in place of the traditional Saint-Venant equations for surface flow. The results suggest that a dynamic model for momentum is preferred over diffusive wave model for shallow coastal wetlands and marshes because the latter fails to capture flow unsteadiness. Under the combined effects of evaporation and wetting/drying, using diffusive wave model leads to discrepancies in modeled surface-subsurface exchange flux in the intertidal zone where strong exchange processes occur. It indicates shallow wetland models should be built with (i) dynamic surface flow equations that capture the timing of inundation, (ii) complex topographic features that render accurate spatial extent of inundation, and (iii) variably-saturated subsurface flow solver that is capable of modeling moisture change in the subsurface due to evaporation and infiltration.

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