Review on thermal energy storage with phase change: materials, heat transfer analysis and applications

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

An introduction to heat transfer

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Numerical Heat Transfer And Fluid Flow

This paper explores the recent research developments in high-heat-flux thermal management. Cooling schemes such as pool boiling, detachable heat sinks, channel flow boiling, microchannel and mini-channel heat sinks, jet-impingement, and sprays, are discussed and compared relative to heat dissipation potential, reliability, and packaging concerns. It is demonstrated that, while different cooling options can be tailored to the specific needs of individual applications, system considerations always play a paramount role in determining the most suitable cooling scheme. It is also shown that extensive fundamental electronic cooling knowledge has been amassed over the past two decades. Yet there is now a growing need for hardware innovations rather than perturbations to those fundamental studies. An example of these innovations is the cooling of military avionics, where research findings from the electronic cooling literature have made possible the development of a new generation of cooling hardware which promise order of magnitude increases in heat dissipation compared to today's cutting edge avionics cooling schemes.

Assessment of high-heat-flux thermal management schemes

\n Film cooling technology is widely used in gas turbines. With the additive manufacturing anticipated in the future, there will be more freedom in film cooling hole design. Exploiting this freedom, the present authors tried using curved holes to generate Dean vortices within the delivery line. These vortices have opposite direction of rotation to the vorticity of the kidney vortices and, thus, there is interaction between these vortices in the mixing region. It is shown that as a result of the inclusion of Dean vortices, the curved hole delivery leads to enhanced film cooling effectiveness. Numerical results, including film cooling effectiveness values, tracking of vortices in the flow field, heat transfer coefficients, and net heat flux reduction (NHFR), are compared between the curved hole, round hole, and a laidback, fan-shaped hole with blowing ratios, M, of 0.5, 1.0, 1.5, 2.0, and 2.5. The comparison shows that film cooling effectiveness values with the curved hole are higher than those with cylindrical film cooling holes at every blowing ratio studied. The curved hole has lower film cooling effectiveness values than the laidback, fan-shaped holes when M = 0.5 and 1.0, but shows advantages when the blowing ratio is higher than 1.0. There is heat transfer enhancement for the curved hole case due to a higher kinetic energy transferred to the near-wall region, however. Nevertheless, the curved hole still displays a higher NHFR when the blowing ratio is high.

Enhancement of Film Cooling Effectiveness Using Dean Vortices

A 2-D axisymmetric computational model was developed to simulate a UMN test rig and encompassing: a piston/cylinder and 90 degree flow turn to a radial flow between two discs. Three cases were studied representing a combination of two disc spacings (54 & 127 mm) and two oscillating frequencies (30 & 70 CPM). The CFD-ACE+ commercial CFD code was utilized for this study. Both laminar and turbulent simulations were attempted. The CFD code was validated by comparing with experimental data for a unidirectional jet impinging on a flat plate. The agreement was good. The laminar and turbulent flow cases mimic closely the flow visualization obtained in the UMN rig. The CFD simulations for the three oscillatory flow cases revealed close similarity of flow features. However, distinct differences were noticed, in both computations and experiments, between small and large disc spacing in the channel. The small channel shows the presence of vortices only in a portion of the cycle. The large channel shows a large vortex throughout the whole cycle. This vortex gets stronger during jetting into the disc space (exhaust stroke) and weaker during suction into the cylinder.

A 2-D axisymmetric CFD model of oscillatory flow with separation

: The low-pressure turbine of an aircraft engine operates with a low chord Reynolds number. As such, there are regions of strong streamwise acceleration and diffusion effects. This results in extended regions of transition from laminar to turbulent flow and large zones of flow separation. In response to a need to learn more about the mechanisms that lead to transition and separation in the engine environment, a low-Reynolds-number-flow study initiated during the Summer of 1994 at Wright Labs. In this project, a low-pressure turbine airfoil cascade was installed in a wind tunnel. To simulate the engine environment, high background turbulence was imposed on the flow and a device for imposing passing wakes upon the flow was fabricated. A program for measurement of the characteristics of the boundary layer; laminar-like or turbulent, separated or attached, was initiated. The Summer project resulted in an effective start on the problem but considerably more remained to be done. This report documents the subsequent work on this project. At the University of Minnesota, an easily accessible facility which had the essential elements of the low-pressure turbine flow was designed, built, and qualified. This facility now provides a convenient means for documenting the flow and developing measurement techniques. The Wright Lab experimental program continued with the completion of the construction, the implementation of the turbulence generating device, and the qualification of the tunnel. Both facilities are now producing data to the program. These data are summarized herein. The University of Minnesota facility has generated pressure profiles for various cases of different Reynolds number and turbulence intensity. The Wright Labs facility has given pressure profiles for various Reynolds numbers.

Separating and Separated Boundary Layers.

We have discussed the force contours produced during dielectric barrier discharge on a plasma actuator. There is asymmetry in the direction and magnitude of forces during cathode directed and anode directed discharges. This can be attributed to the difference in the dielectric charging characteristics during positive and negative pulses. Accurate modeling of surface processes on the dielectric is essential to understanding the working of the actuator. Nomenclature n p e n n n , , = densities of electrons, positive ions, and negative ions n p e D D D , , = species diffusivities n p e µ µ µ , , n p e v v v    , , = species mobility = species velocity r e e , 0

Plasma actuator simulation: Force contours and dielectric charging characteristics

The laminar-turbulent transition process has been documented in a concave-wall boundary layer subject to low (0.6 percent) free-stream turbulence intensity. Transition began at a Reynolds number, Rex (based on distance from the leading edge of the test wall), of 3.5 × 105 and was completed by 4.7 × 105 . The transition was strongly influenced by the presence of stationary, streamwise, Gortler vortices. Transition under similar conditions has been documented in previous studies, but because concave-wall transition tends to be rapid, measurements within the transition zone were sparse. In this study, emphasis is on measurements within the zone of intermittent flow. Twenty-five profiles of mean streamwise velocity, fluctuating streamwise velocity, and intermittency have been acquired at five values of Rex , and five spanwise locations relative to a Gortler vortex. The mean velocity profiles acquired near the vortex downwash sites exhibit inflection points and local minima. These minima, located in the outer part of the boundary layer, provide evidence of a “tilting” of the vortices in the spanwise direction. Profiles of fluctuating velocity and intermittency exhibit peaks near the locations of the minima in the mean velocity profiles. These peaks indicate that turbulence is generated in regions of high shear, which are relatively far from the wall. The transition mechanism in this flow is different from that on flat walls, where turbulence is produced in the near-wall region. The peak intermittency values in the profiles increase with Rex , but do not follow the “universal” distribution observed in most flat-wall, transitional boundary layers. The results have applications whenever strong concave curvature may result in the formation of Gortler vortices in otherwise 2-D flows.

Terrence W. Simon

Papers

Enhancement of Film Cooling Effectiveness Using Dean Vortices

A 2-D axisymmetric CFD model of oscillatory flow with separation

Separating and Separated Boundary Layers.

Plasma actuator simulation: Force contours and dielectric charging characteristics

Measurements in a Transitional Boundary Layer With Görtler Vortices