CFD prediction of vortex breakdown in a rotating cavity with an axial throughflow of air

Experimental evidence has shown that for certain ratios of axial to tangential velocity, at the inlet of a rotating cavity with an axial throughflow of air, vortex breakdown can occur. A non-isothermal, laminar prediction made using computational fluid dynamics techniques (CFD) shows evidence of this. At vortex breakdown the predicted mass flow entering the cavity varies significantly with time.     

Computation of buoyancy-induced flow in a heated rotating cavity with an axial throughflow of cooling air

In the cavity between the co-rotating compressor discs in gas turbine engines, the flow is very complex because of the multiple driving forces including the centrifugal buoyancy force, the Coriolis force and the inertial force. Numerical analysis was carried out in a simple rotating cavity with cooling air axial throughflow and a heated shroud. Efforts were focused upon the flow structure and its variations. The results reveal the non-axisymmetrical flow structures with cyclonic and anti-cyclonic circulations, which slip relative to the rotating cavity in the opposite direction (that is, rotate with a slower speed than the cavity) and the patterns remain unchanged. These structures are not unique, and four types with one, two, three, four pairs of circulations are obtained. For any particular set of conditions, the final structure can depend on the path taken: as axial Reynolds number is increased the number of circulation couples increases, and as Grashof number is increased the number of circulation couples decreases. At high Grashof number, the variation of Nu_av with Gr is consistent with the Rayleigh–Bénard convection.     

Numerical investigation into influence of geometry on flow in a rotating cavity with an axial throughflow

For cooling design, in modern gas turbine engines, it is important to understand and predict the fluid flow and heat transfer in the high pressure compressor drum cavities, which have complex and varying geometries. Unsteady, three dimensional (3-D), Computational Fluid Dynamics (CFD) techniques are used to illustrate the great influence the geometry of these cavities has on flow and heat transfer. Comparisons are made with heat transfer measurements and general agreement is found. Predictions suggest that for certain geometries less computationally expensive axisymmetric CFD or boundary layer integral computations may be suitable for design purposes.     

轴向通流旋转盘腔内类Rayleigh-Benard对流稳定性研究

利用数值模拟的方法对冷气轴向通流旋转盘腔的流动过程进行了研究。研究发现。对应一进口冷气的冒诺教，存在一临界瑞利敷(Rαc)，高于该瑞利教(Rα)。流动出现不稳定现象。且Rα越大，不稳定行为越严重。对于特例，盘腔内的流动可以看成是由类Rayleigh—Benard对流和强迫对流两个区域构成，两个区域通过能量和质量交换相互影响。流动随着Rα的增加从稳态发展为非稳态；采用频谱图分析的方法对数值解的不稳定性进行定性分析。结果显示随着Rα的增大。教值解经历了从稳定解到分贫的周期性不稳定和准周期不稳定的发展过程，离心浮升力引起的类Rayleigh—Benard对流是造成流动从稳定到不稳定发展的重要原因，哥氏力的存在恶化了不稳定过程。     

Convective heat transfer inside a rotating cylinder with an axial air flow

This article presents an experimental identification technique for the convective heat transfer coefficient inside a rotating cylinder with an axial airflow. The method consists in heating the outer face of the cylinder using infrared lamps, and acquiring the evolution of the external surface temperature versus time using an infrared camera. Heat transfer coefficients are identified via three methods. The first one is based on an inverse model, the second one assumes the wall of the cylinder as a thermally thin wall and the third one is based on an analytical method permitting to obtain the temperature field within the whole cylinder. The experiments were carried out for a rotational speed ranging from 4 to 880 rpm corresponding to rotational Reynolds numbers varying from 1.6×10³ to 4.7×10⁵ and an air flow rate varying from 0 to which corresponds to an axial Reynolds numbers ranging from 0 to 3×10⁴. Correlations connecting the Nusselt number to the axial and rotational Reynolds numbers are also proposed.     

Flow development through HP &; LP turbines,Part I: Inward rotating cavity flow with superimposed throughflow

With the aid of numerical method,both flow field and its accompanied loss mechanism within the rotating cavity are investigated in detail in the 1st part of the two parts paper.For ease of comparison,rotating cavity is further classified as the rotor-stator cavity case and the rotor-rotor cavity case.Results indicate that flow within both kinds of the cavity act as the inviscid flow except that the flow near walls,neighboring the lower G region and in the vicinity of the rotating orifices.In the regions except such inviscid-flow-dominate domains,the theoretical core rotation factor can be safely used to predict the swirl ratio within the cavity.When detailed flow pattern is considered,Ekman-type flow exists near periphery of the surface's boundary layer where viscous effect is non-negligible.However,due to the complex profile of the simulated cavity case,vortices structure is varied within the cavity.By comparison,swirl ratio can be used to predict the magnitude of loss.Due to the relatively evident rotating effects of the rotor-rotor cavity,swirl ratio even increases to 1.4 in the current model,which means that flow is moving faster than the surrounding disc.Further investigation finds that this kind of highly rotating flow is accompanied with serious undesirable pressure loss.Parenthetically,unlike its counterpart,swirl ratio above 1.0 doesn't happen when fluid passes through the rotor-stator cavity.So it is suggested that rotor-rotor flow cavity with the superimposed inward throughflow should be avoided in the engine design or certain measurements should be provided when such structure design is unavoidable.Simulation done in the current paper is meaningful since these dimensional parameters are typical in the design of state-of-art.Relatively lower range of Reφ and Cw is not considered in the current two parts paper.     

Mixed convection along a rotating vertical slender cylinder in an axial flow

A general analysis has been developed to study fluid flow and heat transfer characteristics for mixed convection along a rotating vertical slender cylinder. Transformed set of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasilinearisation technique. The effects of rotational, buoyancy and suction/injection parameters have been investigated in the present study. The effects of various parameters on the velocity profiles in x- and θ-directions and the temperature profile are reported in the present study. The buoyancy force causes considerable velocity overshoot for low Prandtl number (Pr) fluids. The Prandtl number (Pr) strongly affects the surface heat transfer rate. Numerical results are presented for the skin friction coefficients in x- and θ-directions and for the Nusselt number.     

Unsteady mixed convection from a rotating vertical slender cylinder in an axial flow

Unsteady mixed convection flow over a rotating vertical slender cylinder under the combined effects of buoyancy force and thermal diffusion with injection/suction has been studied where the slender cylinder is inline with the flow. The effect of surface curvature is also taken into account, especially for the applications such as wire and fiber drawing, where accurate predictions are desired. The governing boundary layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled nonlinear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. The effects of various parameters on velocity and temperature profiles and on skin friction coefficients and heat transfer rate at the wall are reported in the present study.     

Mixed convection heat transfer in a lid-driven cavity with a rotating circular cylinder

Mixed convection heat transfer in a lid-driven cavity with a rotating cylinder was analyzed numerically for two important parameters - Richardson number, the non-dimensional angular velocity of the cylinder, and the direction of rotation using the commercial software, ADINA. The results from these simulations were validated using an open-source spectral element code, Nek5000. The results of this investigation were presented in terms of streamlines, isotherms, and average and local Nusselt numbers. The present results illustrated that the average Nusselt number was found to depend on the direction of the angular velocity. The average Nusselt number increased with an increase in the clockwise angular velocity of the cylinder for various Richardson numbers. However, it decreased with an increase in the counterclockwise until reached a critical velocity where average Nusselt number increased with an increase in the angular velocity. This study illustrated that the maximum heat transfer can be achieved when placing a rotating cylinder inside a cavity compared with non-rotating cylinder.     

Coexisting phenomena of surge and rotating stall in an axial flow compressor

The unsteady inner flow structure of a single-stage axial flow compressor under the coexisting conditions of surge and rotating stall was experimentally investigated via detailed measurements of the unsteady characteristics and the internal flow velocity fluctuations. The main relevant feature of the tested compressor is a shock tube with a capacity tank connected in series to the compressor outlet through slits and a concentric duplex pipe： surge and rotating stall can both be generated by connecting the shock tube. Research attention is focused on the unsteady behavior of a rotating stall during the surge cycle. The size of the rotating stall cell during the recovery process of an irregular surge cycle was experimentally determined by the circumferential flow velocity fluctuations ahead of the rotor blade. The results suggested that the size of the rotating stall cell at the switching point of the performance curve between large and small cycles is considered to be the key parameter in determining the following surge cycle. In addition, the surge cycle is largely influenced by the unsteady behavior of the rotating stall cell.     

Unsteady behavior of surge and rotating stall in an axial flow compressor

Unsteady behaviors as well as unsteady cascade flow fields of a single-stage axial flow compressor were experimentally investigated by detail measurements of unsteady performance characteristics and casing wall pressure and internal flow velocity fluctuations. The main feature of the test compressor is a capacity tank connected directly to the compressor outlet in series through slits and a concentric duplex pipe, and also jet nozzles in order to inject compressed air toward the rotor tip region. Research attention is focused on the post-stall characteristics of surge and rotating stall which occur simultaneously. When the compressor was connected to the capacity tank, surge was generated with rotating stall in accordance with the capacitance increment of whole compressor system. The surge behavior changed irregularly with throttling valve installed behind the compressor, and several types of surge cycles were observed. In addition, the surge cycle changed by jet injection to the rotor tip region. The results suggested that the blockages of the cascade flow which were generated by a stall cell play an important role in deciding the surge behaviors.     

Thermal stresses in radiant tubes due to axial,circumferential and radial temperature distributions

This paper presents an analysis of the thermal stresses in radiant tubes. The analytical analysis is verified using a finite element model. It was found that axial temperature gradients are not a source of thermal stresses as long as the temperature distribution is linear. Spikes in the axial temperature gradient are a source of high thermal stresses. Symmetric circumferential gradients generate thermal stresses, which are low as compared to the stress rupture value of radiant tubes. Radial temperature gradients create bi-axial stresses and can be a major source of thermal stress in radiant tubes. A local hot spot generates stresses, which can lead to failure of the tube.     

Convective heat transfer combined with surface radiation in a rotating square cavity with a local heater

The effect of surface radiation on laminar natural convection in a rotating cavity with a discrete heater has been analyzed numerically. The enclosure is insulated at the bottom and top, heated by a constant temperature from the discrete heater located on the bottom wall, and cooled by a constant temperature from the side walls. Governing equations with corresponding initial and boundary conditions formulated in dimensionless stream function, vorticity, and temperature have been solved by finite difference method of the second-order accuracy. The effects of surface emissivity, Rayleigh number, and Taylor number on the fluid flow and heat transfer have been studied. Obtained results have revealed that rotation can be a very good control parameter for heat transfer and fluid flow.     

An axial heat transfer analytical model for capillary-pumped loop vapor line temperature distributions

This paper aims to study the capillary-pumped loop (CPL) vapor line temperature distributions. A simple axial heat transfer method is developed to predict the vapor line temperature from evaporator outlet to condenser inlet. CPL is a high efficiency two-phase heat transfer device. Since it does not need any other mechanical force such as pump, furthermore, it might be used to do the thermal management of high power electronic component such as spacecraft, notebook and computer servers. It is a cyclic circulation pumped by capillary force, and this force is generated from the fine porous structure in evaporator. A novel semi-arc porous evaporator to CPL in 1U server is designed on the ground with a horizontal position and scale down the whole device to the miniature size. From the experimental results, the CPL could remove heat 90 W in steady-state and keep the heat source temperature about 70 °C. Finally, a good agreement between the simulation and experimental values has been achieved. Comparing with experiment and simulation results, the deviation values of the distributions of the condenser inlet temperature are less than 8%.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one, two and three undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one-, two- and three-undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.     

Mixed convection inside a fluid‐porous composite cavity with centrally rotating cylinder

The mixed convection in a fluid‐porous composite medium lying inside a square cavity with a centrally rotating cylinder has been investigated in the present work. The bottom half of the cavity is filled with a porous material and the top half is filled with a clear fluid. The bottom wall of the cavity is at a higher temperature, and the top wall is at a lower temperature. The vertical walls are thermally insulated. The convection inside the cavity sets through the combined mechanisms of the thermal buoyancy force and the shearing action of the centrally rotating cylinder. The relative importance of each driving mechanism over the other is featured through the Richardson number. The Darcy–Brinkman–Forchheimer equation is used for the flow modeling in the porous medium, and a single‐domain approach is adopted for the numerical solution in the fluid‐porous composite medium. The simulation is carried out with ANSYS Fluent software, and a parametric analysis involving the Rayleigh number (), Richardson number (), and the Darcy number () is conducted showing their effects on the flow and heat transfer. The phenomena are quite interesting at higher Darcy number and Rayleigh number. The distributions of isotherms, streamlines, and vector plots are plotted, along with the local Nusselt numbers for different parameters, to explore the underlying physics of the phenomenon. The system is found stable at lower Darcy number, and the heat transfer is minimum around Ri = 10. From the numerical study, an empirical correlation for the average Nusselt number is developed as a function of the other dimensionless numbers.     

Melting of a vertical ice cylinder inside a rotating cylindrical cavity filled with binary aqueous solution

The melting of a vertical ice cylinder into a homogeneous calcium chloride aqueous solution inside a rotating cylindrical cavity with several rotating speeds is considered experimentally. The melting mass and temperature are measured on four initial conditions of the solution and four rotating speeds of the cavity. The temperature of the liquid layer becomes uniform by the mixing effect resulting from cavity rotation and it enhances the melting rate of the ice cylinder. As the cavity‐rotating speed increases, the melting rate increases. The dimensionless melting mass is related to the Fourier number and the rotating Reynolds number in each initial condition, therefore an experimental equation that is able to quantitatively calculate the dimensionless melting mass is presented. It is seen that the melting Nusselt numbers increase again in the middle of the melting process. The ice cylinder continues to melt in spite of the small temperature difference between the ice cylinder and the solution. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(6): 359–373, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20211     

Thermal instability of a power-law fluid-saturated porous layer with an internal heat source and vertical throughflow

The thermal instability of internally heated convection in a porous medium saturated by a power-law (PL) fluid is studied. The governing dimensionless equations are solved using the normal mode approach, which leads to an eigenvalue problem for the linear stability theory. The neutral curves are obtained for different prescribed values of the other physical parameters. The effect of the PL index, internal heat source parameter, and Peclet number on the onset of instability was analyzed. Furthermore, an analytical solution is obtained for the regime of small wave numbers by using asymptotic analysis.