Use of Fin Equation to Calculate Nusselt Numbers for Rotating Disks

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Hui Tang ◽  
Tony Shardlow ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Circular Disk ◽  
Rotating Disk ◽  
Conjugate Problem ◽  
Temperature Measurements ◽  
Rotating Disks ◽  
Nusselt Numbers ◽  
Induced Flow ◽  
Thin Disks

Conduction in thin disks can be modeled using the fin equation, and there are analytical solutions of this equation for a circular disk with a constant heat-transfer coefficient. However, convection (particularly free convection) in rotating-disk systems is a conjugate problem: the heat transfer in the fluid and the solid are coupled, and the relative effects of conduction and convection are related to the Biot number,  Bi, which in turn is related to the Nusselt number. In principle, if the radial distribution of the disk temperature is known then Bi  can be determined numerically. But the determination of heat flux from temperature measurements is an example of an inverse problem where small uncertainties in the temperatures can create large uncertainties in the computed heat flux. In this paper, Bayesian statistics are applied to the inverse solution of the circular fin equation to produce reliable estimates of Bi for rotating disks, and numerical experiments using simulated noisy temperature measurements are used to demonstrate the effectiveness of the Bayesian method. Using published experimental temperature measurements, the method is also applied to the conjugate problem of buoyancy-induced flow in the cavity between corotating compressor disks.

Use of Fin Equation to Calculate Nusselt Numbers for Rotating Discs

2015 ◽  
Author(s):  
Hui Tang ◽  
Tony Shardlow ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Conjugate Problem ◽  
Temperature Measurements ◽  
Rotating Disc ◽  
Nusselt Numbers ◽  
Rotating Discs ◽  
Induced Flow ◽  
Buoyancy Induced Flow

Conduction in thin discs can be modelled using the fin equation, and there are analytical solutions of this equation for a circular disc with a constant heat-transfer coefficient. However, convection (particularly free convection) in rotating-disc systems is a conjugate problem: the heat transfer in the fluid and the solid are coupled, and the relative effects of conduction and convection are related to the Biot number, Bi, which in turn is related to the Nusselt number. In principle, if the radial distribution of the disc temperature is known then Bi can be determined numerically. But the determination of heat flux from temperature measurements is an example of an inverse problem where small uncertainties in the temperatures can create large uncertainties in the computed heat flux. In this paper, Bayesian statistics are applied to the inverse solution of the circular fin equation to produce reliable estimates of Bi for rotating discs, and numerical experiments using simulated noisy temperature measurements are used to demonstrate the effectiveness of the Bayesian method. Using published experimental temperature measurements, the method is also applied to the conjugate problem of buoyancy-induced flow in the cavity between corotating compressor discs.

Measurement and Analysis of Buoyancy-Induced Heat Transfer in Aero-Engine Compressor Rotors

2020 ◽  
Author(s):  
Richard W. Jackson ◽  
Dario Luberti ◽  
Hui Tang ◽  
Oliver J. Pountney ◽  
James A. Scobie ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Three Dimensional ◽  
Outer Region ◽  
Conjugate Problem ◽  
Radial Temperature ◽  
Nusselt Numbers ◽  
Induced Flow ◽  
Aero Engines ◽  
Inner Region ◽  
Buoyancy Induced Flow

Abstract The flow inside cavities between co-rotating compressor discs of aero-engines is driven by buoyancy, with Grashof numbers exceeding 1013. This phenomenon creates a conjugate problem: the Nusselt numbers depend on the radial temperature distribution of the discs, and the disc temperatures depend on the Nusselt numbers. Furthermore, Coriolis forces in the rotating fluid generate cyclonic and anti-cyclonic circulations inside the cavity. Such flows are three-dimensional, unsteady and unstable, and it is a challenge to compute and measure the heat transfer from the discs to the axial throughflow in the compressor. In this paper, Nusselt numbers are experimentally determined from measurements of steady-state temperatures on the surfaces of both discs in a rotating cavity of the Bath Compressor-Cavity Rig. The data are collected over a range of engine-representative parameters and are the first results from a new experimental facility specifically designed to investigate buoyancy-induced flow. The radial distributions of disc temperature were collected under carefully-controlled thermal boundary conditions appropriate for analysis using a Bayesian model combined with the equations for a circular fin. The Owen-Tang buoyancy model has been used to compare predicted radial distributions of disc temperatures and Nusselt numbers with some of the experimentally determined values, taking account of radiation between the interior surfaces of the cavity. The experiments show that the average Nusselt numbers on the disc increase as the buoyancy forces increase. At high rotational speeds the temperature rise in the core, created by compressibility effects in the air, attenuates the heat transfer and there is a critical rotational Reynolds number for which the Nusselt number is a maximum. In the cavity, there is an inner region dominated by forced convection and an outer region dominated by buoyancy-induced flow. The inner region is a mixing region, in which entrained cold throughflow encounters hot flow from the Ekman layers on the discs. Consequently, the Nusselt numbers on the downstream disc in the inner region tend to be higher than those on the upstream disc.

Measurement and Analysis of Buoyancy-Induced Heat Transfer in Aero-Engine Compressor Rotors

2020 ◽  
Author(s):  
Richard Jackson ◽  
Dario Luberti ◽  
Hui Tang ◽  
Oliver J Pountney ◽  
James Scobie ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Three Dimensional ◽  
Conjugate Problem ◽  
Radial Temperature ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
First Results ◽  
Engine Compressor ◽  
Induced Flow ◽  
Aero Engines

Abstract The flow inside cavities between co-rotating compressor discs of aero-engines is driven by buoyancy, with Grashof numbers exceeding 1013. This phenomenon creates a conjugate problem: the Nusselt numbers depend on the radial temperature distribution of the discs, and the disc temperatures depend on the Nusselt numbers. Furthermore, Coriolis forces in the rotating fluid generate cyclonic and anti-cyclonic circulations inside the cavity. Such flows are three-dimensional, unsteady and unstable, and it is a challenge to compute and measure the heat transfer from the discs to the axial throughflow in the compressor. In this paper, Nusselt numbers are experimentally determined from measurements of steady-state temperatures on the surfaces of both discs in a rotating cavity of the Bath Compressor-Cavity Rig. The data are collected over a range of engine-representative parameters and are the first results from a new experimental facility specifically designed to investigate buoyancy-induced flow. The radial distributions of disc temperature were collected under carefully-controlled thermal boundary conditions appropriate for analysis using a Bayesian model combined with the equations for a circular fin. The Owen-Tang buoyancy model has been used to compare predicted radial distributions of disc temperatures and Nusselt numbers with some of the experimentally determined values, taking account of radiation between the interior surfaces of the cavity. The experiments show that the average Nusselt numbers on the disc increase as the buoyancy forces increase. At high rotational speeds the temperature rise in the core, created by compressibility effects in

scholarly journals Buoyancy-Induced Flow and Heat Transfer in Compressor Rotors

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Hui Tang ◽  
Mark R. Puttock-Brown ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Temperature Rise ◽  
Radial Growth ◽  
Radial Clearance ◽  
Rotating Disks ◽  
Compressor Blades ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Induced Flow ◽  
Buoyancy Induced Flow

The buoyancy-induced flow and heat transfer inside the compressor rotors of gas-turbine engines affects the stresses and radial growth of the compressor disks, and it also causes a temperature rise in the axial throughflow of cooling air through the center of the disks. In turn, the radial growth of the disks affects the radial clearance between the rotating compressor blades and the surrounding stationary casing. The calculation of this clearance is extremely important, particularly in aeroengines where the increase in pressure ratios results in a decrease in the size of the blades. In this paper, a published theoretical model—based on buoyancy-induced laminar Ekman-layer flow on the rotating disks—is extended to include laminar free convection from the compressor shroud and forced convection between the bore of the disks and the axial throughflow. The predicted heat transfer from these three surfaces is then used to calculate the temperature rise of the throughflow. The predicted temperatures and Nusselt numbers are compared with measurements made in a multicavity compressor rig, and mainly good agreement is achieved for a range of Rossby, Reynolds, and Grashof numbers representative of those found in aeroengine compressors. Owing to compressibility effects in the fluid core between the disks—and as previously predicted—increasing rotational speed can result in an increase in the core temperature and a consequent decrease in the Nusselt numbers from the disks and shroud.

Numerical Investigation of Heat Transfer in Rectangular Microchannels Under H2 Boundary Condition During Developing and Fully Developed Laminar Flow

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
V. V. Dharaiya ◽  
S. G. Kandlikar
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Fluid Flow ◽  
Microfluidic Devices ◽  
Transport Processes ◽  
Uniform Heat Flux ◽  
Data Set ◽  
Nusselt Numbers ◽  
Aspect Ratios

Study of fluid flow characteristics at microscale is gaining importance with shrinking device sizes. Better understanding of fluid flow and heat transfer in microchannels will have important implications in electronic chip cooling, heat exchangers, MEMS, and microfluidic devices. Due to short lengths employed in microchannels, entrance header effects can be significant and need to be investigated. In this work, three dimensional model of microchannels, with aspect ratios (α = a/b) ranging from 0.1 to 10, are numerically simulated using CFD software tool fluent. Heat transfer effects in the entrance region of microchannel are presented by plotting average Nusselt number as a function of nondimensional axial length x*. The numerical simulations with both circumferential and axial uniform heat flux (H2) boundary conditions are validated for existing data set for four wall heat flux case. Large numerical data sets are generated in this work for rectangular cross-sectional microchannels with heating on three walls, two opposing walls, one wall, and two adjacent walls under H2 boundary condition. This information can provide better understanding and insight into the transport processes in the microchannels. Although the results are seen as relevant in microscale applications, they are applicable to any sized channels. Based on the numerical results obtained for the whole range, generalized correlations for Nusselt numbers as a function of channel aspect ratio are presented for all the cases. The predicted correlations for Nusselt numbers can be very useful resource for the design and optimization of microchannel heat sinks and other microfluidic devices.

scholarly journals Effects of the rotation number on flow and heat transfer in contra-rotating disk cavity with superposed flow

2019 ◽  
Vol 11 (10) ◽  
pp. 168781401988104 ◽  
Author(s):  
Shu-xian Chen ◽  
Jing-zhou Zhang
Keyword(s):  
Heat Transfer ◽  
Flow Structure ◽  
Rotation Number ◽  
Tangential Velocity ◽  
Inertial Force ◽  
Rotating Disk ◽  
Rotating Disks ◽  
Radial Temperature ◽  
Disk Rotation ◽  
Type Flow

The turbulent fluid flow and convective heat transfer in counter-rotating disk cavity with central axial air inflow and radial air outflow are numerically studied based on the finite volume method. Efforts are focused upon the influence of the rotation number Rt on the flow structure, cooling performance, sealing effect, and surface tangential friction characteristics in the cavity. The stagnation point where the radial outward flow along the upstream disk driven by the rotation force meets the radial outward flow along downstream disk driven by the combination of rotation force and inflow inertial force moves from upstream disk wall to the shroud with increasing Rt. At the Rt far smaller than 1, the fluids in the core region between two disks rotate with the upstream disk like a rigid body, and the tangential velocity of the rotating core decreases with the increase of the disk cavity radius, which is different from the Batchelor-type flow. At the Rt larger than 1, the fluids on the upstream disk side rotate like the Batchelor-type flow, while the sandwich rotation disappears in the fluid on the downstream disk side. The temperature on the upstream disk wall increases and then decreases with increasing values of Rt, and the critical value of Rt for the change of temperature variation is assessed to be at about Rt = 0.69. The temperature and radial temperature gradient of the downstream disk wall decrease with increasing Rt. With increasing Rt by increasing the disk rotation rate, the pressures near the downstream disk decrease, while the frictional moments on rotating disks increase. Due to the effect of flow structure, the frictional moment on the upstream disk is smaller than that on the downstream disk.

Heat Transfer in a “Cover-Plate” Preswirl Rotating-Disk System

1999 ◽  
Vol 121 (2) ◽  
pp. 249-256 ◽  
Author(s):  
R. Pilbrow ◽  
H. Karabay ◽  
M. Wilson ◽  
J. M. Owen
Keyword(s):  
Heat Transfer ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Turbine Disk ◽  
Cover Plate ◽  
Blade Cooling ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Cooling Air ◽  
Plate System

In most gas turbines, blade-cooling air is supplied from stationary preswirl nozzles that swirl the air in the direction of rotation of the turbine disk. In the “cover-plate” system, the preswirl nozzles are located radially inward of the blade-cooling holes in the disk, and the swirling airflows radially outward in the cavity between the disk and a cover-plate attached to it. In this combined computational and experimental paper, an axisymmetric elliptic solver, incorporating the Launder–Sharma and the Morse low-Reynolds-number k–ε turbulence models, is used to compute the flow and heat transfer. The computed Nusselt numbers for the heated “turbine disk” are compared with measured values obtained from a rotating-disk rig. Comparisons are presented, for a wide range of coolant flow rates, for rotational Reynolds numbers in the range 0.5 X 106 to 1.5 X 106, and for 0.9 < βp < 3.1, where βp is the preswirl ratio (or ratio of the tangential component of velocity of the cooling air at inlet to the system to that of the disk). Agreement between the computed and measured Nusselt numbers is reasonably good, particularly at the larger Reynolds numbers. A simplified numerical simulation is also conducted to show the effect of the swirl ratio and the other flow parameters on the flow and heat transfer in the cover-plate system.

Effects of Creep Flow and Viscous Dissipation in the Slip Regime for Isoflux Rectangular Microchannels

2007 ◽  
Author(s):  
Jennifer van Rij ◽  
Tim Ameel ◽  
Todd Harman
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Pressure Drop ◽  
Convective Heat Transfer ◽  
Viscous Dissipation ◽  
Convective Heat ◽  
Numerical Algorithm ◽  
Slip Flow ◽  
Creep Flow ◽  
Nusselt Numbers

The effects of rarefaction on convective heat transfer and pressure drop characteristics are numerically evaluated for uniform wall heat flux rectangular microchannels. Results are obtained by numerically solving the momentum and energy equations with both first- and second-order slip velocity and temperature jump boundary conditions. The resulting velocity and temperature fields are then evaluated to obtain the microchannel Poiseuille and Nusselt numbers. In addition to the effects of rarefaction, the effects of aspect ratio, thermal creep flow, and viscous dissipation are investigated for locally fully developed Poiseuille and Nusselt numbers. The constant wall heat flux results obtained in this study are compared to constant wall temperature results obtained previously, using the same numerical algorithm, at various aspect ratios including the limiting case of parallel plate microchannels. In addition to supplying previously unreported data on slip flow convective heat transfer and pressure drop characteristics, these results verify the numerical algorithm for more complex future slip flow analyses.

Conjugate Heat Transfer in a Rotor-Stator System With Through-Flow

2002 ◽  
Author(s):  
Reby Roy ◽  
B. V. S. S. S. Prasad ◽  
S. Srinivasa Murthy
Keyword(s):  
Heat Transfer ◽  
Boundary Layer Thickness ◽  
Conjugate Heat Transfer ◽  
Rotating Disk ◽  
Thermal Boundary Layer Thickness ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
Commercial Code ◽  
Through Flow

The conjugate heat transfer in a stationary cylindrical cavity with a rotating disk and fluid through-flow is analysed at various rotational speeds ranging from 10000 to 50000 rpm by using a finite volume commercial code. The numerical model and code are validated for a problem, which involves rotation and fluid through-flow. A reduction of the thermal boundary layer thickness and increase in the heat transfer coefficients are observed with increase in the rotational speed. Marked differences are noticed between the Nusselt numbers obtained from the conjugate and constant temperature analyses.

Investigation on Convective Heat Transfer over a Rotating Disk with Bottom Wall Subjected to Uniform Heat Flux

2012 ◽  
Vol 249-250 ◽  
pp. 443-451
Author(s):  
Jing Zhou Zhang ◽  
Xiao Ming Tan ◽  
Xing Dan Zhu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Study ◽  
Rotating Disk ◽  
Outer Radius ◽  
Bottom Wall ◽  
Uniform Heat Flux ◽  
Uniform Heat

A three-dimensional numerical study on the flow and heat transfer characteristics over a rotating disk with bottom wall subjected to uniform heat flux was conducted with the use of RNG k- turbulent model. And some experiments were also made for validation. The effects of rotating angular speed and pin configuration on the temperature maps and convective heat transfer characte-ristics on rotating surface are analyzed. As the increase of rotating velocity, the impingement of pumping jet on the centre of rotating disk became stronger and the transition from laminar to turbu-lent occurred at the outer radius of rotating disk, which resulted in heat transfer enhancement. The pins on the disk made the pumping action of a rotating disk weaker. Simultaneously, they also acted as disturbing elements to the cyclone flow near the rotating disk surface, which made the overall heat transfer to be enhanced. Under the same extend areas of different pins, needle pin has higher convective heat transfer capacity than the discrete ring pin.

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