The linear wave instability of boundary layer flow induced by a horizontal heated surface in porous media

In this paper we use the parallel-flow approximation to determine the criterion for the onset of instability in the form of travelling waves in a horizontal thermal boundary layer in porous media. We find that waves grow beyond a nondimensional distance of 28.90 from the leading edge, a result which shows, somewhat surprisingly, that waves are to be preferred over vortices, which have been found to grow beyond 33.47 from the leading edge [1]. We discuss very briefly the implications of our analysis for the use of the parallel flow approximation in the determination of stability criteria for thermal boundary layers.     

Large eddy simulation of transition of free convection flow over an inclined upward facing heated plate

Transition of free convection flow of air over an inclined heated surface is investigated numerically by using a large eddy simulation method. In particular, we focus on how inclination angle of an upward-facing heated plate affects flow transition. Special attention is paid to the development of the thermal boundary layer and the transition from the laminar to turbulent stage. Results show that the transition occurs early when the plate is moved from its vertical position due to the rapid growth of both the velocity and thermal boundary layers. As a consequence, the critical Grashof number drops. Effects of the inclination of plate on the turbulent velocity fluctuations are also investigated, and the predicted results are in very good agreement with various experimental data available in the literature.     

Thermal receptivity of free convective flow from a heated vertical surface: Linear waves

Numerical techniques are used to study the receptivity to small-amplitude thermal disturbances of the boundary layer flow of air which is induced by a heated vertical flat plate. The fully elliptic nonlinear, time-dependent Navier–Stokes and energy equations are first solved to determine the steady state boundary-layer flow, while a linearised version of the same code is used to determine the stability characteristics. In particular we investigate (i) the ultimate fate of a localised thermal disturbance placed in the region near the leading edge and (ii) the effect of small-scale surface temperature oscillations as means of understanding the stability characteristics of the boundary layer. We show that there is a favoured frequency of excitation for the time-periodic disturbance which maximises the local response in terms of the local rate of heat transfer. However the magnitude of the favoured frequency depends on precisely how far from the leading edge the local response is measured. We also find that the instability is advective in nature and that the response of the boundary layer consists of a starting transient which eventually leaves the computational domain, leaving behind the large-time time-periodic asymptotic state. Our detailed numerical results are compared with those obtained using parallel flow theory.     

The linear stability of a developing thermal front in a porous medium: The effect of local thermal non-equilibrium

In this paper we analyze the stability of the developing thermal boundary layer which is induced by a step-change in the temperature of the lower horizontal boundary of a uniformly cold semi-infinite porous medium. Particular attention is paid to the influence of local thermal non-equilibrium between the fluid and solid phases and how this alters the stability criterion compared with corresponding criterion when the phases are in local thermal equilibrium. A full linear stability analysis is developed without approximation, and this yields a parabolic system of equations for the evolving disturbances. Criteria for the onset of convection are derived as a function of the three available nondimensional parameters, the inter-phase heat transfer coefficient, H, the porosity-scaled conductivity ratio, γ, and the diffusivity ratio, α.     

The effect of longitudinal surface waves on free convection from vertical surfaces in porous media

In this paper we consider the effect of longitudinal surface waves on the thermal boundary layer flow induced by a vertically aligned heated surface embedded in a porous medium. The full governing equations are considered and the boundary layer equations are derived in a systematic way. It is found that, for a wide range of values of x, the distance from the leading edge, the boundary layer equations for the three—dimensional flowfield are satisfied by a two-dimensional similarity solution.     

Transition of natural convection boundary layers—a revisit by Bicoherence analysis

Previous studies have revealed that heat transfer through a convective thermal boundary layer can be significantly enhanced by perturbing the thermal boundary layer to advance linear to nonlinear transition. It has also been demonstrated that the enhancement of heat transfer is mostly achieved in the nonlinear regime. In this study, the transition of the thermal boundary layer adjacent to an isothermally heated vertical surface is revisited by means of Bicoherence analysis, which is a statistical approach for identifying and quantifying quadratic wave interactions. The streamwise evolution of Bicoherence spectra suggests that the thermal boundary layer can be classified into three regimes: a linear flow regime, a transitional flow regime and a nonlinear flow regime. The positions of the transition from the transitional to nonlinear regimes in the thermal boundary layer at various Rayleigh numbers, perturbation frequencies and perturbation amplitudes are determined using Bicoherence analysis. It is found that in the nonlinear flow regime, the number of resonance groups fluctuates, which indicates the occurrence of coupling and decoupling of harmonics in the boundary layer. This process may be the mechanism responsible for the resonance induced enhancement of heat transfer.     

Vortical structures and heat transfer augmentation of a cooling channel in a gas turbine blade with various arrangements of tip bleed holes

Abstract

This study investigates the internal cooling processes affected by the tip bleed holes in gas turbine blades. Double bleed holes are fixed at the center of the blade tip near the pressure side and suction side, respectively. Five different arrangements of the holes along the center line of the tip are studied. The purely double holes are set as the Baseline. The purpose of the present study is to provide a new perspective of the tip film cooling to understand the internal flow processes, vorticity evolution and the mechanism of the heat transfer augmentation. A topological analysis and the boundary layer analysis methods are introduced to better understand the tip heat transfer. The total extraction area and volume is kept at the same level for all the studied cases. The results show that the Dean vortices and the near-wall vortices induced by the secondary flow contribute to the high heat transfer coefficient on the tip surface. The mixing effect of the Dean vortices and the hole extraction helps to enhance heat transfer upstream of the tip. Different arrangement of the bleed holes can affect the internal flow processes and heat transfer performance. The suction effect of the center-line bleed hole can accelerate the near-hole flow and reduce the thickness of the boundary layer. The center-line hole fitted at the middle of the tip affects significantly the rear side of the hole. Thus, the holes aligned in the middle of the tip provide the highest heat transfer and thermal performance. The thermal performance is enhanced by up to 4.7% compared with the Baseline.     

Effect of oblique shock wave induced from a wavy-wall combustor surface for a splitter plate scramjet combustor

The shorter residence period of supersonic air in a scramjet combustor makes mixing and combustion challenging. Mixing augmentation occurs at the fuel-supersonic air interface. Multiple interactions between shock waves and the shear layer may significantly affect this inter surface. In this research, an attempt has been made to analyze how multiple oblique shock waves interact with the shear layer. The primary splitter plate combustor bottom wall is modified with a wavy-wall surface to ensure the development of multiple oblique shock waves. The internal flow field with and without a wavy wall surface has been analyzed by solving the two-dimensional Reynolds averaged Navier-Stokes equations and SST k-ω turbulence model. The reaction between ethylene fuel and the air is modeled with a global one-step reaction mechanism with finite rate eddy dissipation turbulence chemistry interaction. The flow disturbances with the wavy-wall surface have been evaluated by analyzing the numerical results like the flow structure, pressure, velocity, reaction rate, vortices, turbulence intensity, and interactions among shock wave, shear mixing, and boundary layers. The oblique shock waves induced from the wavy-wall surface significantly impact the mixing of fuel and air and successful reaction mechanism from the visualization of flow structure and concern results.     

Vortex instability of natural convection flow on inclined surfaces

The linear stability of laminar natural convection flow adjacent to a heated, inclined, upwardfacing plate is investigated for disturbances having the form of longitudinal vortices. The stability problem is formulated with account being taken of the fact that the basic flow and temperature fields depend on the streamwise coordinate. One of the demonstrated consequences of retaining the transverse velocity of the basic flow is the so-called bottling effect, wherein the disturbance vorticity and temperature are contained within the respective boundary layers of the basic flow. The calculated neutral stability curves exhibit an altogether different character depending upon whether the streamwise dependence of the basic flow and temperature fields is taken into account or suppressed; the magnitude of the critical Grashof numbers from the two models differs by several orders of magnitude. The results also show that the greater the inclination of the plate from the vertical, the more susceptible is the flow to the vortex-type instability.The relationship of the analytical results to available experimental information is discussed.     

Transient thermal stability in fluid layers with non-uniform volumetric energy sources

The thermal stability of a horizontal fluid layer in its transient conduction mode is studied. The critical Rayleigh numbers which characterise the onset of convection are determined using linear stability theory. The fluid is heated internally by absorption of the external radiation penetrating downwards into the fluid. The effects of optical thickness and boundary conditions are also investigated.     

Onset of surface tension driven convection in a fluid layer overlying a layer of an anisotropic porous medium

The paper deals with the criterion for the onset of surface tension-driven convection in the presence of temperature gradients in a two-layer system comprising a fluid saturated anisotropic porous layer over which lies a layer of fluid. The lower rigid surface is assumed to be insulated to temperature perturbations, while at the upper non-deformable free surface a general thermal condition is invoked. Both the Beavers-Joseph and the Jones conditions have been used at the interface to know their preference and prominence in the study of the problem. The resulting eigenvalue problem is solved exactly and also by regular perturbation technique when both the boundaries are insulating to temperature perturbations. It is found that the depth of the relative layers, mechanical and thermal anisotropy parameters have a profound effect on the stability of the system. Decreasing the mechanical anisotropy parameter and increasing the thermal anisotropy parameter leads to stabilization of the system. Besides, the possibility of control of Marangoni convection by suitable choice of physical parameters is discussed in detail.     

Numerical study and control method of interaction of nucleation and boundary layer separation in condensing flow

The spontaneous nucleation flow in turbine cascade was numerically studied. The model was implemented within a full Navier–Stokes viscous flow solution procedure and the process of condensation was calculated by the quadrature method of moments that shows good accuracy with very broad size distributions. Results were presented for viscous and inviscous flow, showing the influence of boundary layer separation and wake vortices on spontaneous nucleation. The results show that the degree of flow separation in wet steam flow is greater than that in superheated steam flow due to condensation shock and that the loss cannot be neglected. Furthermore, the impact of boundary layer separation and wake vortices on velocity profiles and its implications for profile loss were considered. The calculations showed that layer separation and wake vortices influence nucleation rate, leading to different droplet distributions. A method for controlling homogeneous nucleation and for reducing degree of flow separation in high-speed transonic wet steam flow was presented. The liquid phase parameter distribution is sensitive to the suction side profile of turbine cascade, which impacts the nucleation rate distribution leading to different droplet distributions and affects the degree of flow separation. The numerical study provides a practical design method for turbine blade to reduce wetness losses.     

Preliminary experiments on the control of natural convection in differentially-heated cavities

Aiming at the control of natural convection flows and heat transfer in air-filled differentially-heated cavities, experimental attempts were carried out in order to achieve the stability of such flows to various excitations. The mechanism of control chosen in these experiments introduces thermal disturbances via a thin pipe located inside the boundary layer at the bottom of the hot wall. Its temperature varies periodically due to alternating electrical heating and continuous water cooling. The effects of this disturbance in temperature are investigated for a Rayleigh number value chosen just greater than the first bifurcation value from a steady state flow to a monoperiodic state. The results show the distribution of the overall and local Nusselt numbers. The introduction of this obstacle induces a 10% decrease in heat transfer. Temperature oscillations of the actuator provoke modifications of the flow field. In particular, an amplification of unsteadiness in the outer borders of boundary layers is observed and a displacement of secondary vortices is encountered. Explanations are given by a detailed examination of flow structures, such as the spatial distribution of velocities and their fluctuations.     

Numerical study and control method of interaction of nucleation and boundary layer separation in condensing flow

The spontaneous nucleation flow in turbine cascade was numerically studied. The model was implemented within a full Navier-Stokes viscous flow solution procedure and the process of condensation was calculated by the quadrature method of moments that shows good accuracy with very broad size distributions. Results were presented for viscous and inviscous flow, showing the influence of boundary layer separation and wake vortices on spontaneous nucleation. The results show that the degree of flow separation in wet steam flow is greater than that in superheated steam flow due to condensation shock and that the loss cannot be neglected. Furthermore, the impact of boundary layer separation and wake vortices on velocity profiles and its implications for profile loss were considered. The calculations showed that layer separation and wake vortices influence nucleation rate, leading to different droplet distributions. A method for controlling homogeneous nucleation and for reducing degree of flow separation in high-speed transonic wet steam flow was presented. The liquid phase parameter distribution is sensitive to the suction side profile of turbine cascade, which impacts the nucleation rate distribution leading to different droplet distributions and affects the degree of flow separation. The numerical study provides a practical design method for turbine blade to reduce wetness losses.     

Transition to a periodic flow induced by a thin fin on the sidewall of a differentially heated cavity

The transition to a periodic flow induced by a thin fin on the sidewall of a differentially heated cavity is numerically investigated. The numerical results are compared with a previously reported experiment. It is demonstrated that the transient flow obtained numerically shows features consistent with the experimental flow. Based on the present numerical results, the temporal development and spatial structures of the thermal flow around the fin are described, and the separation of the thermal flow above the fin is discussed. It is found that the presence of the fin changes the flow regime and results in the transition of the thermal flow to a periodic flow. The present numerical results also indicate that the unstable temperature configuration above the fin results in intermittent plumes at the leeward side of the fin, which in turn induce strong oscillations of the downstream boundary layer flow. It is demonstrated that the oscillations of the boundary layer flow significantly enhance the heat transfer through the finned sidewall (by up to 23%).     

Effect of moving distance of a moving block on heat transfer in a channel flow

A numerical investigation of heat transfer rate of an insulated block moving on a heated surface in a channel was studied. The study mainly investigated the effect of block moving distance on the heat transfer rate of heated surface. This subject belongs to a kind of moving boundary problems, and the modified Arbitrary Lagrangian Eulerian method is suitable for solving this subject. The results show that the block moving distance affects the flow and thermal fields remarkably. The heat transfer rate of heated surface increases proportionally to the increment of the block moving distance, when the block moving distance is larger than a critical value.     

Secondary flow and forced convection heat transfer near endwall boundary layer fences in a 90° turning duct

The present study deals with the secondary flow and heat transfer aspects of endwall boundary layer fences in 90° turning ducts. Boundary layer fences have recently been re-introduced as additional components to achieve favorable aerothermal effects in turbine/compressor passages and internal cooling systems. The turbine passage or internal coolant channel is simulated by a 90° turning duct (Re_D=360,000) to study the aerothermal interaction of the boundary layer fence and the passage flow that is dominated by the passage vortices. Specifically, a single boundary layer fence of varying dimensions is attached to a heated endwall of the duct. The current study adds to the currently small number of investigations on the use of endwall boundary layer fences and their aerothermal interaction with the passage flow system.     

Enhancement of Heat Transfer Using Delta-Winglet Type Vortex Generators with a Common-Flow-up Arrangement

Simulations of a coolant air flowing in a heat exchanger with delta-winglet type vortex generators in common-flow-up configuration have been performed to unveil the salient heat transfer characteristics. The heat exchanger is approximated as a periodic rectangular channel with heated walls and a pair of built-in tubes near the inlet and outlet. The heat transfer characteristics of the heat exchangers with vortex generators near the inlet, outlet, and both inlet and outlet have been compared. The Navier-Stokes equations together with the energy equation are solved employing unstructured finite volume method. The simulations reveal a significant enhancement in heat transfer because of the strong swirling motion originating from the streamwise longitudinal vortices behind the pair of delta winglets. The spiraling flow entrains air into the core and causes intermixing of the fluid layers to disrupt the growth of the thermal boundary layer. A parametric study on the angles of attack identifies the conditions under which enhancement in heat transfer can lead to significant miniaturization of the heat exchangers. The analysis also reveals interesting flow structures behind the winglets and correlates them to the mechanism of heat transfer.