scholarly journals A Kolmogorov-like exact relation for compressible polytropic turbulence

2014 ◽  
Vol 742 ◽  
pp. 230-242 ◽  
Author(s):  
Supratik Banerjee ◽  
Sébastien Galtier
Keyword(s):  
Sound Speed ◽  
Transfer Rate ◽  
Inertial Range ◽  
Compressible Turbulence ◽  
Polytropic Index ◽  
Energy Transfer Rate ◽  
Exact Relation ◽  
Point Correlation ◽  
The Mean ◽  
High Reynolds

AbstractCompressible hydrodynamic turbulence is studied under the assumption of a polytropic closure. Following Kolmogorov, we derive an exact relation for some two-point correlation functions in the asymptotic limit of a high Reynolds number. The inertial range is characterized by: (i) a flux term implying in particular the enthalpy; and (ii) a purely compressible term $\mathcal{S}$ which may act as a source or a sink for the mean energy transfer rate. At subsonic scales, we predict dimensionally that the isotropic $k^{-5/3}$ energy spectrum for the density-weighted velocity field ($\rho ^{1/3} \boldsymbol {v}$), previously obtained for isothermal turbulence, is modified by a polytropic contribution, whereas at supersonic scales $\mathcal{S}$ may impose another scaling depending on the polytropic index. In both cases, it is shown that the fluctuating sound speed is a key ingredient for understanding polytropic compressible turbulence.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

Extraction of energy transfer rate constants from the pulsed laser generated thermal lens spectrometer signal

1982 ◽  
Vol 80 ◽  
pp. 433-436 ◽  
Author(s):  
R.T. Bailey ◽  
F.R. Cruickshank ◽  
R. Guthrie ◽  
D. Pugh ◽  
I.J.M. Weir
Keyword(s):  
Energy Transfer ◽  
Thermal Lens ◽  
Rate Constants ◽  
Transfer Rate ◽  
Pulsed Laser ◽  
Energy Transfer Rate

scholarly journals Research on the design and application of capillary heat exchangers for heat pumps in coastal areas

2021 ◽  
Vol 42 (3) ◽  
pp. 333-348
Author(s):  
Zhenpeng Bai ◽  
Yanfeng Li ◽  
Jin Zhang ◽  
Alan Fewkes ◽  
Hua Zhong
Keyword(s):  
Renewable Energy ◽  
Energy Transfer ◽  
Heat Exchanger ◽  
Heat Pump ◽  
Transfer Rate ◽  
Coastal Areas ◽  
Heat Energy ◽  
Low Carbon ◽  
Energy Transfer Rate ◽  
Pump System

This study investigated the optimal design of a capillary heat exchanger device for the heat pump system and its innovative engineering application in a building. The overall aim was to use a capillary heat exchanger to obtain energy in coastal areas for promoting renewable energy in low-carbon building design. Initially, the main factors affecting the efficiency of the capillary heat exchanger were identified, a mathematical model was then established to analyse the heat transfer process. The analysis showed the flow rate and the capillary length are the key factors affecting the efficiency of the capillary heat exchanger. Secondly, to optimize the structural design of the capillary heat exchanger, the heat energy transfer is calculated with different lengths of the capillary under various flow rates in summer and winter conditions, respectively. Thirdly, a typical building is selected to analyse the application of the capillary heat exchanger for extracting energy in the coastal area. The results show the performance of the selected capillary heat exchanger heat pump system, in winter, the heat energy transfer rate is 60 W/m2 when the seawater temperature is 3.7 °C; in summer, the heat energy transfer rate is 150 W/m2 when the seawater temperature is 24.6 °C. Finally, the above field test results were examined using a numerical simulation model, the test and simulation results agree with each other quite well. This paper is conducive in promoting the development of the capillary heat exchanger heat pump as an innovative sustainable technology for net-zero energy and low carbon buildings using renewable energy in coastal areas. Practical application: A recently proposed capillary heat exchanger is used as an energy extraction and utilisation device to obtain energy in coastal areas for promoting renewable energy in low-carbon building design. This paper explores the application of a capillary heat exchanger as both cold and heat sources for application in typical low-rise buildings. The analysis of the heat energy transfer rate of a typical low-rise building located in a coastal area in summer and winter provides guidance for the application of capillary heat exchangers.

A Numerical Study of Three-Dimensional Natural Convective Heat Transfer From a Plate With a “Wavy” Surface

2001 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Matt Garrett
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Surface Waves ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Wavy Surface ◽  
Surface Waviness ◽  
Dimensionless Amplitude ◽  
The Mean

Abstract Natural convective heat transfer from a wide isothermal plate which has a “wavy” surface, i.e., has a surface which periodically rises and falls, has been numerically studied. The surface waves run parallel to the direction of flow over the surface and have a relatively small amplitude. Two types of wavy surface have been considered here — saw-tooth and sinusoidal. Surfaces of the type considered are approximate models of situations that occur in certain window covering applications, for example, and are also sometimes used to try to enhance the heat transfer rate from the surface. The flow has been assumed to be laminar. Because the surface waves are parallel to the direction of flow, the flow over the surface will be three-dimensional. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq type approximation. The governing equations have been written in dimensionless form, the height of the surface being used as the characteristic length scale and the temperature difference between the surface temperature and the temperature of the fluid far from the plate being used as the characteristic temperature. The dimensionless equations have been solved using a finite-element method. Although the flow is three-dimensional because the surface waves are all assumed to have the same shape, the flow over each surface thus being the same, and it was only necessary to solve for the flow over one of the surface waves. The solution has the following parameters: the Grashof number based on the height, the Prandtl number, the dimensionless amplitude of the surface waviness, the dimensionless pitch of the surface waviness, and the form of the surface waviness (saw-tooth or sinusoidal). Results have been obtained for a Prandtl number of 0.7 for Grashof numbers up to 106. The effects of Grashof number, dimensionless amplitude and dimensionless pitch on the mean heat transfer rate have been studied. It is convenient to introduce two mean heat transfer rates, one based on the total surface area and the other based on the projected frontal area of the surface. A comparison of the values of these quantities gives a measure of the effectiveness of the surface waviness in increasing the mean heat transfer rate. The results show that while surface waviness increases the heat transfer rate based on the frontal area, the modifications of the flow produced by the surface waves are such that the increase in heat transfer rate is less than the increase in surface area.

Improvement of Er3+:4I11/2→Ce3+:2F5/2 energy transfer rate in Er3+/Ce3+ co-doped TeO2–ZnO–Na2O–Nb2O5 glasses

2009 ◽  
Vol 129 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Yaxun Zhou ◽  
Jun Wang ◽  
Shixun Dai ◽  
Tiefeng Xu ◽  
Qiuhua Nie ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Transfer Rate ◽  
Energy Transfer Rate ◽  
Co Doped

Experimental evaluation of the mean momentum and kinetic energy balance equations in turbulent pipe flows at high Reynolds number

2019 ◽  
Vol 20 (5) ◽  
pp. 285-299 ◽  
Author(s):  
El-Sayed Zanoun ◽  
Christoph Egbers ◽  
Ramis Örlü ◽  
Tommaso Fiorini ◽  
Gabriele Bellani ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Energy Balance ◽  
Kinetic Energy ◽  
Experimental Evaluation ◽  
High Reynolds Number ◽  
Balance Equations ◽  
Pipe Flows ◽  
The Mean ◽  
High Reynolds

scholarly journals Numerical Simulations of Encounters of Hard Binaries

1985 ◽  
Vol 113 ◽  
pp. 335-338
Author(s):  
Seppo Mikkola
Keyword(s):  
Cross Sections ◽  
Transfer Rate ◽  
Binding Energies ◽  
Body System ◽  
Energy Transfer Rate ◽  
Orbital Elements ◽  
Numerical Integrations ◽  
Order Of Magnitude ◽  
Three Body ◽  
Theory And Experiments

Results from numerical integrations of random binary-binary encounters have been used to obtain various cross-sections and outcome distributions for the four-body scattering. The initial orbital elements were chosen randomly except the Kepler-energies for which various selected values were used. Rough estimates for mass effects were obtained by simulating encounters of binaries with unequal component masses.We developed a semi-analytical theory for obtaining the types and energies of the outcome configurations. The theory contains some adjustable parameters, the values of which we deduced by comparing the theory and experiments.The energy transfer rate by collisions (=outcome is not two binaries) dominates over that due to fly-by's by an order of magnitude, provided that the binaries are hard. The formation of a hierarchical three-body system is fairly common. In a collision of energetically similar very hard binaries the probability is about 20 percent, while it is greater than 50 percent if the binding energies differ by a factor of more than four.

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