Throughflow Reynolds Number Research Articles

Instability of Poiseuille Flow in a Bidisperse Porous Medium Subject to a Uniform Vertical Throughflow Effect

Abstract In this article, we investigate the influence of the vertical throughflow Reynolds number on the instability of Poiseuille flow in a bidisperse porous medium. The Brinkman model was employed to describe fluid flow in the porous medium with large pores, referred to as “macropores,” while the Darcy model was utilized for fluid flow in the porous medium with small pores, referred to as “micropores”. The resulting eigenvalue system was solved using the Chebyshev collocation method (CCM), renowned for its accuracy and flexibility, rendering it one of the most reliable methods available. Regardless of its direction, the impact of the vertical throughflow Reynolds number on system instability is not uniform; it exhibits a dual nature, acting as a destabilizing factor at specific values while serving as a stabilizing influence at others. In the case of the permeability ratio, porous parameter, and interaction parameter, our observations indicate that elevating these parameters results in an enhancement of system stability.

Comparative Thermal Performances between Pumped Thermosyphon Loops with Different Condenser Configurations Using R245fa as Working Fluid

A pumped two-phase thermosyphon loop is broadly utilized to intensify the cooling duties of electronic chipsets/systems and the effectiveness for harvesting thermal energy. The configuration of a condenser not only affects the heat transfer in the condenser, but also has an effect on the saturation pressures during the boiling and condensation processes to alter the hydrothermal performance of a pumped thermosyphon loop. The influence of the condenser configuration on the hydrothermal performance of a pumped thermosyphon loop is rarely studied. The present study comparatively examined the thermal performances of two pumped thermosyphon loops with a conventional tube-fin condenser and the expansion-tank condenser. The thermodynamic cycles in pressure-temperature and pressure-enthalpy diagrams, Nusselt numbers of evaporator and condenser, thermal resistances and various performance indexes evaluated at constant pumping powers at the controlled through-flow Reynolds numbers, boiling numbers and condenser thermal resistances were measured. At the similar thermal loads, flow rates, and fluid entry temperatures of condenser, the operating pressure of the thermosyphon loop with expansion tank condenser was considerably reduced from that with tube fin condenser, leading to the lower saturation temperature for reducing the thermal resistance and the lesser pressure drop across the loop with a noticeable hydrothermal performance improvement. At the parametric conditions tested, the ratio of dimensionless overall thermal resistances between the loops with expansion tank condenser and tube fin condenser fell in the range of 0.81–0.99. When the loop performance was compared at a constant cooling airflow rate without considering the more pumping power consumption for the loop with tube fin condenser, the ranges of thermal resistance for the loops with expansion tank condenser and tube fin condenser were 0.13–0.21 (KW−1) and 0.15–0.23 (KW−1). The merit indices evaluating the comparative hydrothermal performances of evaporator, condenser and loop between the two looped thermosyphons highlighted the significance of condenser design and affirmed the performance improvement by changing tube fin condenser into expansion tank condenser. The empirical correlations of evaporator Nusselt number, condenser Nusselt number, and overall thermal resistance using Reynolds number, boiling number, and condenser thermal resistance as the controlling parameters were generated for relevant applications.

An investigation on the forced convection heat transfer in the gap of two rotating disks with laminar inflow

AbstractThis study presents forced convection in the gap between two rotating disks with the laminar radial inward flow. The disk surfaces are held at a constant temperature different from the temperature of the fluid flowing. The disks' surfaces may also receive a heat flux. The temperature of the fluid flowing in the gap is predicted by solving the coupled equations of momentum, energy, and continuity in cylindrical coordinate numerically. The finite difference method is used to discretize the energy equation into nonlinear algebraic equations. The tridiagonal matrix algorithm is employed to solve the resulting algebraic equations. Predominantly, throughflow Reynolds number, rotational Reynolds number, gap ratio, speed ratio, and Peclet number are the parameters that affect the temperature distribution for the fixed disk temperature and for the heat flux boundary conditions. The Nusselt number compares reasonably well with the numerical results of other investigators. The heat flow into the fluid is higher for corotating disks than for contrarotating disks for both constant temperatures as well as heat flux boundary conditions. This is the first investigation that predicts temperature distribution due to forced convection in the gap of two rotating disks with laminar inflow.

Ekman Layer Scrubbing and Shroud Heat Transfer in Centrifugal Buoyancy-Driven Convection

Abstract This paper presents large-eddy and direct numerical simulations of buoyancy-driven convection in sealed and open rapidly rotating cavities for Rayleigh numbers in the range 107–109, and axial throughflow Reynolds numbers 2000 and 5600. Viscous heating due to the Ekman layer scrubbing effect, which has previously been found responsible for the difference in sealed cavity shroud Nusselt number predictions between a compressible N–S solver and an incompressible counterpart using the Boussinesq approximation, is discussed and scaled up to engine conditions. For the open cavity with an axial throughflow, laminar Ekman layer behavior of the mean flow statistics is confirmed up to the highest condition in this paper. The Buoyancy number Bo is found useful to indicate the influence of an axial throughflow. For the conditions studied the mean velocities are subject to Ra, while the velocity fluctuations are affected by Bo. A correlation, Nu′=0.169(Ra′)0.318, obtained with both the sealed and open cavity shroud heat transfer solutions, agrees with that for free gravitational convection between horizontal plates within 16% for the range of Ra′ considered.

An Investigation on Forced Convection in Clearance of Corotating Disks With Diverging Laminar Flow

Abstract In this work, forced convection in the laminar outflow between two disks is predicted. The disks can be corotating or contrarotating with equal or with different angular velocities. A published closed form solution is used to model the forced convection. The simplified energy equation is discretized using a finite difference method. The discretized equation is solved using the tridiagnal matrix algorithm (TDMA). Results are obtained for a heat flux as well as a specified temperature boundary condition and are presented for various flow parameters such as throughflow Reynolds number, rotational Reynolds number, gap ratio and speed ratio. The parameters except the speed ratio affect the temperature field strongly. The computed Nusselt number is in good agreement with the published experimental data. The coupling of closed form solution and energy equation predicts temperature field accurately. Additionally, the solution procedure is simplified considerably and the solution is obtained with lesser computational resources.

Theoretical Investigation on Inflow Between Two Rotating Disks

Mathematical relations are obtained for velocities and pressure distribution for a fluid entering the peripheral clearance of a pair of rotating concentric disks that converges and discharges through an opening at the center. Both, the flows in the gap of corotating disks and in the gap of contrarotating disks can be predicted using the present analytical solutions. The prediction of instability of radial velocity for corotating disks at the speed ratio of unity is very important for practical applications. The radial velocity profile is similar to a parabolic profile exactly at speed ratio of unity. The profile drastically changes with the small difference of ±1% in the disks’ rotation. The radial convection was observed in the tangential velocity at a low radius. Centrifugal force caused by disk rotation highly influences the flow resulting in backflow on the disks. The pressure consists of friction losses and convective inertia. Therefore, the pressure decrease is high for increased speed ratio, throughflow Reynolds number, and rotational Reynolds number. The pressure decrease for the flow between contrarotating disks is lesser than that for the flow between corotating disks due to decreased viscous losses in the tangential direction. This study provides valuable guidance for the design of devices where disks are rotated independently by highlighting the instabilities in the radial velocity at the speed ratio of unity.

Closed Form Solution for Outflow Between Corotating Disks

Mathematical expressions are derived for flow velocities and pressure distributions for a laminar flow in the gap between two rotating concentric disks. Fluid enters the gap between disks at the center and diverges to the outer periphery. The Navier–Stokes equations are linearized in order to get closed-form solution. The present solution is applicable to the flow between corotating as well as contrarotating disks. The present results are in agreement with the published data of other investigators. The tangential velocity is less for contrarotating disks than for corotating disks in core region of the radial channel. The flow is influenced by rotational inertia and convective inertia both. Dominance of rotational inertia over convective inertia causes backflow. Pressure depends on viscous losses, convective inertia, and rotational inertias. Effect of viscous losses on pressure is high at small throughflow Reynolds number. The convective and rotational inertia influence pressure significantly at high throughflow and rotational Reynolds numbers. Both favorable and unfavorable pressure gradients can be found simultaneously depending on a combination of parameters.

On the stability of internally heated natural convection due to the absorption of radiation in a laterally confined fluid layer with a horizontal throughflow

This study focuses on the marginal stability of the natural convection flow induced by the absorption of radiation. Non-uniform internal heating associated with the absorption of radiation following Beer’s law and the absorption and re-emission of residual radiation by the bottom boundary wall lead to a nonlinear base temperature profile that evolves with time. A horizontal throughflow and lateral confinement are incorporated in the analysis, and two forms of convective instability, i.e. longitudinal and transverse rolls, are investigated. It is shown that the formation of longitudinal rolls, with their axes parallel to the throughflow direction, is not affected by the presence of the throughflow. For transverse rolls, with their axes perpendicular to the throughflow direction, however, the throughflow is shown to have a stabilising effect, with the critical Rayleigh number increasing with the increasing throughflow Reynolds number. It follows that longitudinal rolls are the preferred form of instability in laterally unconfined domains for any nonzero Reynolds number and in confined domains if the Reynolds number is greater than a critical value. The value of the critical Reynolds number, which separates the preferred mode of instability, is found to rapidly reduce with increasing lateral extent and approaches zero for a normalised lateral extent greater than 2.0. The lateral confinement is also shown to have a stabilising effect for both longitudinal and transverse rolls, with the critical Rayleigh number increasing with the reducing lateral extent. It is shown that the lateral confinement only substantially affects the wave number of the rolls with their axes parallel to the confining walls but not the rolls with their axes perpendicular to the confining walls.

Inward Flow Between Stationary and Rotating Disks

The present study predicts the flow field and the pressure distribution for a laminar flow in the gap between a stationary and a rotating disk. The fluid enters through the peripheral gap between two concentric disks and converges to the center where it discharges axially through a hole in one of the disks. Closed form expressions have been derived by simplifying the Navier– Stokes equations. The expressions predict the backflow near the rotating disk due to the effect of centrifugal force. A convection effect has been observed in the tangential velocity distribution at high throughflow Reynolds numbers.

Windage Heating in a Shrouded Rotor-Stator System.

This paper has experimentally and numerically studied the windage heating in a shrouded rotor-stator disk system with superimposed flow. Temperature rise in the radius direction on the rotating disk is linked to the viscous heating process when cooling air flows through the rotating component. A test rig has been developed to investigate the effect of flow parameters and the gap ratio on the windage heating, respectively. Experimental results were obtained from a 0.45 m diameter disk rotating at up to 12,000 rpm with gap ratio varying from 0.02 to 0.18 and a stator of the same diameter. Infrared temperature measurement technology has been proposed to measure the temperature rise on the rotor surface directly. The PIV technique was adapted to allow for tangential velocity measurements. The tangential velocity data along the radial direction in the cavity was compared with the results obtained by CFD simulation. The comparison between the free disk temperature rise data and an associated theoretical analysis for the windage heating indicates that the adiabatic disk temperature can be measured by infrared method accurately. For the small value of turbulence parameter, the gap ratio has limited influence on the temperature rise distribution along the radius. As turbulence parameter increases, the temperature rise difference is independent of the gap ratio, leaving that as a function of rotational Reynolds number and throughflow Reynolds number only. The PIV results show that the swirl ratio of the rotating core between the rotor and the stator has a key influence on the windage heating.

Windage Measurements in a Rotor-Stator System With Superimposed Cooling and Rotor-Mounted Protrusions

This paper has experimentally studied the windage torque in a rotor-stator system with superimposed central inflow and rotor-mounted protrusions. A novel measurement method has been proposed, and the basic principle is to transform the torque of rotating components into static torque measured by using a static torquemeter. Compared with the previous research, the difference of the moment coefficient for the free plain disk in this paper is within 10%. The disk models used in the experiments included a plain disk and a rotor with 18 protrusions. Plain-disk results were obtained with axial clearances varying from 4.5 mm to 40.5 mm and a stator of the same diameter. Two test cases were performed: one was the case where the flow structure was dominated by the superimposed flow and the other was where rotation dominated the flow structure. For the plain-disk case, as turbulence parameter increases, the sensitivity of the torque to variations of G value also increases, leaving the moment coefficient as a function of the rotational and throughflow Reynolds number only. Comparing to the flow parameter, gap ratio and shroud-clearance ratio have weaker influence on frictional moment coefficient. The rotor with protrusions results showed that the gap ratio had negligible effect on the moment coefficient for the former case; however, the torque decreased by approximately 20% with the decrease of the gap ratio for the latter case. It was also found that, for different configurations, the deviation in the moment coefficient was attributed to variations in form drag. In addition, the moment coefficient was affected by the orientation of bolts with respect to the direction of rotation. The empirical correlations have been proposed for the windage losses of various bolt configurations, and a further discussion about minimizing the windage losses was conducted.

Heat and fluid flow in cylindrical and conical annular flow-passages with through flow and inner-wall rotation

The flow and heat transfer in cylindrical and conical annular flow-passages with through flow and inner-wall rotation have been numerically simulated by using the large eddy simulation with a Lagrangian dynamic subgrid-scale model. Inlet through-flow Reynolds number was 1000 and the Taylor number was set at 0, 1000, 2000, and 4000. In the conical flow passage, when the inner-wall rotation speed was increased, at first spiral vortices in the downstream region and then much more complicated vortices appeared. The vortices for Ta = 4000 changed the structure in both through-flow and wall-normal directions in the downstream half of the passage. The flow structure and heat transfer of the conical case were completely different from those of the cylindrical case. It was because of the three factors: the expansion of the flow passage, the rotation radius change in the through-flow direction, and the centrifugally driven through-flow. The last factor is due to the acute angle between the centrifugal and through-flow directions.

Windage sources in smooth-walled rotating disc systems

This article presents experimental data and an associated correlation for the windage resulting from a disc rotating in air, characteristic of gas turbine engines and relevant to some electrical machine applications. A test rig has been developed that uses an electric motor to drive a smooth bladeless rotor inside an enclosed pressurized housing. The rig has the capability of reaching rotational and throughflow Reynolds numbers representative of a modern gas turbine. A moment coefficient has been used to allow a non-dimensional windage torque parameter to be calculated and an agreement with the relevant data in the literature has been found within 10 per cent. Infrared measurements have been performed that allow direct surface temperatures of the rotating disc to be obtained. Laser Doppler anemometry measurements have been made that allow velocities in the flow field of the rotor—stator cavity to be examined and tangential velocities corresponding to rotationally and radially dominated flow conditions are shown. The importance of the flow regime in relation to the resulting windage has been identified and in particular it is noted that windage is a function not only of the ratio of rotational and radial flow dominance as defined by the turbulence parameter, but also for a given value of the turbulence parameter, the magnitude of the rotationally induced and superimposed flows. The experiments extend the range of data available for windage in rotor—stator systems and have been used to produce a correlation suitable for applications operating up to the range of Reψ=107.

Localized perturbations in binary fluid convection with and without throughflow

Dynamics and structure of spatially localized convective perturbations in binary fluid layers heated from below and the effect of a plane horizontal Poiseuille throughflow on them are investigated. Fronts and pulse-like wave packets formed out of the three relevant perturbations-two oscillatory ones and a stationary one-are analyzed after evaluating the appropriate saddle points of the three respective dispersion relations of the linear field equations over the complex wave number plane. Front and pulse properties are elucidated in quantitative detail as a function of small throughflow Reynolds numbers for different Soret coupling strengths psi including the pure fluid limit psi=0 in comparison with the appropriate Ginzburg-Landau amplitude equation approximations. Furthermore, small amplitude pulses and fronts obtained from solving the full nonlinear field equations numerically are presented to check and compare with the linear results.

Transient effects of orthogonal pipe oscillations on laminar developing incompressible flow

This paper presents a numerical study of the transient developing laminar flow of a Newtonian incompressible fluid in a straight horizontal pipe oscillating around the vertical diameter at its entrance. The flow field is influenced by the tangential and Coriolis forces, which depend on the through-flow Reynolds number, the oscillation Reynolds number and the angular amplitude of the pipe oscillation. The impulsive start of the latter generates a transient pulsating flow, whose duration increases with axial distance. In any cross-section, this flow consists of a pair of symmetrical counter-rotating vortices, which are alternatively clockwise and anti-clockwise. The circumferentially averaged friction factor and the axial pressure gradient fluctuate with time and are always larger than the corresponding values for a stationary pipe. On the other hand, local axial velocities and local wall shear stress can be smaller than the corresponding stationary pipe values during some part of the pipe oscillation. The fluctuation amplitude of these local variables increases with axial distance and can be as high as 50% of the corresponding stationary pipe value, even at short distances from the pipe entrance. Eventually, the flow field reaches a periodic regime that depends only on the axial position. The results show that the transient flow field depends on the pipe oscillation pattern (initial position and/or direction of initial movement). Copyright © 2000 John Wiley & Sons, Ltd.

Flow and heat transfer in a pipe containing a coaxially-rotating disk

A numerical investigation was made of steady laminar flow and convective heat transfer in a pipe constricted by a coaxially rotating disk. The analysis was executed by using the finite volume approach. Calculations were made for the through-flow Reynolds numbers (based on the pipe radius) of 10, 25, 50, 75, 100, 125, 150, the rotational Reynolds numbers of 0, 250, 500 and 1000, for the disk-to-pipe radius ratios of 0.9, 0.95 and 0.99, and for the Prandtl numbers of 0.7 and 7. The heat transfer rate, the pressure drop coefficient, and the temperature distributions are determined. The results show that the temperature and flow characteristics are substantially affected by the rotation of the disk. In the disk downstream-flow, the wall and disk recirculation zones are noticed. The swirl imparted to the flow measurably increases the heat transfer rate. The increase is especially noticeable when the wall recirculation region does not exist. Physical rationalizations are made of the computed flow features, and a brief description is given of the Nusselt number distribution.

Transient effects of orthogonal pipe oscillations on laminar developing incompressible flow

We present a numerical study of the transient developing laminar flow of a Newtonian incompressible fluid in a straight horizontal pipe oscillating around the vertical diameter at its entrance. The flow field is influenced by the tangential and Coriolis forces, which depend on the through-flow Reynolds number, the oscillation Reynolds number and the angular amplitude of the pipe oscillation. The impulsive start of the latter generates a transient pulsating flow, whose duration increases with axial distance. In any cross-section, this flow consists of a pair of symmetrical counter-rotating vortices, which are alternatively clockwise and anti-clockwise. The circumferentially averaged friction factor and the axial pressure gradient fluctuate with time and are always larger than the corresponding values for a stationary pipe. On the other hand, local axial velocities and local wall shear stress can be smaller than the corresponding stationary pipe values during some part of the pipe oscillation. The fluctuation amplitude of these local variables increases with axial distance and can be as high as 50% of the corresponding stationary pipe value, even at short distances from the pipe entrance

Flow and Heat Transfer in Rotating Cavities.

One of the promising trends to increase the thermal efficiency of gas turbines is to raise the gas temperature at the turbine inlet. In modern gas turbines, turbine section operates under severe thermal conditions. Cooling of the turbine section is one of the key technologies for further improvement of gas turbines to keep their safe working. The objective of this study is to investigate the flow and heat transfer in a low-pressure turbine which has cavities formed by an assembly of turbine disks. This study employs two dimensionless parameters which govern flow and heat transfer in rotating cavities. These are throughflow Reynolds number and rotational Reynolds number. Flow visualization and heat transfer experiments in rotating situation were carried out in wide range of experimental conditions. This paper focuses on the effect of forced convection by the throughflow on flow and heat transfer characteristics in rotating cavities.

B222 貫流を伴う複数の回転キャビティ内の流れと熱伝達特性

This work is related to the fluid flow and heat transfer of rotating cavities in gas turbine engines. In this study flow visualization and heat transfer experiments were carried out. The local heat transfer characteristics of disk surfaces were investigated for two different rotational Reynolds numbers, Reω=0 and 3.0×10 4, at a constant throughflow Reynolds number, Reγ=450. Flow visualization experiments revealed that the Nusselt number distribution depended on the flow structure inside the rotating cavity. Moreover, the flow behavior was quantitatively evaluated by a PIV technique.

Experimental Studies and Correlations of Convective Heat Transfer in a Radially Rotating Serpentine Passage

The present paper investigates experimentally the effects of rotation on the convective heat transfer of air flow in a radially rotating three-passage serpentine square channel. Due to rotation, the cross-stream and radial secondary flows are induced by the Coriolis force and the centrifugal-buoyancy force, respectively. The channel walls were made of low thermal conductivity material for suppressing wall heat conduction. The wall surfaces were heated individually by four separate stainless-steel film heaters to distinguish the local heat transfer rates. The hydraulic diameter and the mean rotational radius of the flow passages were 4 and 180 mm, respectively. The governing parameters are the through-flow Reynolds number Re, the rotation number Ro, the buoyancy parameter Gr* and the main flow direction. The results show that the local heat transfer rate was enhanced by rotation on the trailing side for outward flow and on the leading side for inward flow. In the first and third passages, the effect of rotation on heat transfer is relatively prominent. The buoyancy effect is favorable to the heat transfer enhancement on four sides of these passages. The data of NuΩ/Nu0 are correlated on the leading and trailing sides of these passages.