Numerical simulation of vortex structures and heat transfer behind a hill in a laminar boundary layer

The present study examines a three‐dimensional numerical simulation of vortex structures and heat transfer behind a hill mounted in a laminar boundary layer. A vortex pair is formed symmetrically in the separation bubble behind the hill, and a hairpin vortex is periodically shed in the wake. The hairpin vortex moves downstream with time, and the gradient of the head of the hairpin vortex increases. Further downstream, the hairpin vortex is deformed to an Ω‐shaped structure. In the growth process of the hairpin vortex, horn‐shaped secondary vortices grow near the wall. The dissipation rate of the temperature fluctuation around the hairpin vortex increases because the heated fluid near the wall is removed to the free stream by Q2 ejection. Heat transfer increases due to the legs of the hairpin vortex and secondary vortices. These vortices generate high turbulence in the flow field and also contribute to an increase in Reynolds shear stress and turbulent heat flux. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(7): 398–411, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20217     

层流脉动流中平行圆柱体的温度边界层

采用数值模拟方法研究了一个平行圆柱体在层流脉动流中的温度边界层特性。数值模拟结果与实验数据一致。研究发现脉动流中平行圆柱体形成了形状不规则但相对稳定的温度边界层,并在流动方向上周期性脉动。脉动流中平行圆柱体的温度边界层平均厚度小于稳定流动下的温度边界层平均厚度,并以脉动流的频率进行脉动。此外, 脉动流中平行圆柱体的壁面温度小于稳定流动下的壁面温度,表明脉动流下圆柱体的对流传热得到了强化。在一个脉动周期内,圆柱体在后半周期的温度边界层厚度和热阻均小于前半周期的温度边界层厚度和热阻。     

Improved velocity and temperature profiles for integral solution in the laminar boundary layer flow on a semi‐infinite flat plate

One of the most important problems in Mechanical Engineering is the determination of laminar boundary layer thickness over a flat plate. Integral solution and similarity solutions are two well‐known methods for calculation of boundary layer thickness. However, integral solution method is a computational cost‐effective method rather than the similarity solution method. Velocity and temperature profiles must be determined for the integral solution method. Velocity boundary layer thickness can be determined by the velocity profile whereas for determination of thermal boundary layer thickness both velocity and temperature profiles must be used. Available velocity profiles do not give an exact value for velocity boundary layer thickness, while the Nusselt number is affected by these profiles. In this study, a new velocity profile is proposed which gives an exact value for laminar boundary layer thickness on a flat plate. In addition, two temperature profiles are proposed that give the exact values of the Nusselt number over a flat plate for uniform temperature and uniform heat flux boundary conditions. The calculated constants in the velocity boundary layer thickness equation and the Nusselt relations are validated with the results of the similarity solution method. Excellent agreement between the results of the two methods is observed.     

Coherent structures in a fully developed stage of a non‐isothermal round jet

Direct numerical simulation (DNS) was performed for a non‐isothermal air jet with a Reynolds number of 1200 in order to reveal coherent structures of the developed jet. A fourth‐order central finite difference was applied to the simulation. An effort was also made to enable experimental visualization (dye mixing and PTV) to support the validity of the instantaneous structures by DNS. Computational results for two types of inlet profiles suggested that nozzle conditions scarcely affect the turbulence statistics and the coherent structures in a jet‐established stage. Two‐point correlations of velocity and temperature show that similar distributions denoting the temperature can be used as an indicator of a vortex. A conceptual model of a hairpin‐shaped vortex was proposed and validated by two‐point correlations and PDF analysis for vortex alignment. The hairpin‐shaped vortex stands with legs inclined downstream. The inclination angle and the tilting angle between the two legs are ?45° and 40°, respectively. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(5): 342–356, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20014     

Similarity Solutions of Momentum and Energy Equations for an Axi-symmetric Laminar Jet

A theoretical analysis for momentum and heat transfer characteristics in a steady narrow axisymmetric laminar jet is made based on the assumption of boundary layer. The types of potential flows necessary for having the similar solutions to boundary layer equations are determined and the analytical solutions are presented for both momentum and energy boundary layer equations. Some transport properties of the jets are investigated     

Momentum and heat transfer in laminar boundary layer behind shock wave

Analytical and numerical solutions are established for momentum and energy laminar boundary layer induced by a shock wave. The results indicated that skin friction σ decreases with increasing in velocity ratio ξ(1≤ξ< 6). For each specified ξ(1≤ξ< 6), temperature w(t) increases with increasing of Tw but decreases with Te , and for a range of t ∈[1,ξ], w(t) decreases with the increasing of t. Thermal diffusion increases with increasing of uw but decreases with increasing Ue.     

Perturbation of a laminar boundary layer by a synthetic jet for heat transfer enhancement

An experimental investigation of a cross-flow interaction between a synthetic jet and a flat plate laminar boundary layer is reported. The synthetic jet uses a piezo-actuator for displacing the diaphragm, thus enabling flow control in terms of the excitation amplitude and the modulation frequency. The role of these parameters on heat transfer enhancement from the flat plate is investigated. Measurements are carried out using hotwire anemometry for the flow field while the heat transfer coefficient and jet spreading are imaged respectively by liquid crystal thermography and the laser schlieren technique.Results show that the average heat transfer coefficient increases with excitation amplitude and a maximum of 44% enhancement is observed. Amplitude modulation at low frequencies also increases the heat transfer coefficient. Overall, the study indicates the efficacy of a synthetic jet actuator for heat transfer enhancement with excitation amplitude and modulation frequency as control parameters.Visualization using liquid crystal thermography shows dual streaks over the flat surface indicating the footprint of vortical structures from the synthetic jet inside the laminar boundary layer. The role played by amplitude modulation in enhancing heat transfer is clearly demonstrated by schlieren visualization and further confirmed by hotwire measurements. The synthetic jet also increases the average turbulence content inside the boundary layer. Power spectra show an overall increase in the amplitude of the low frequency fluctuations arising from synthetic jet actuation. The time-averaged velocity profile behind the synthetic jet shows similarity to the wake profile behind a surface-mounted obstacle. Analogous to physical obstacles such as ribs, these results show that a synthetic jet can also be used as a device for heat transfer enhancement in a boundary layer.     

Suitable Heat Transfer Model for Self-Similar Laminar Boundary Layer in Power Law Fluids

The classical power law non-Newtonian fluids energy boundary layer equation is proved improper to describe the self-similar heat transfer. A theoretical analysis for momentum and energy boundary layer transfer behavior is made and the full similarity heat boundary layer equation is developed, which may be characterized by a power law relationship between shear stress and velocity gradient with the Falkner-Skan equation as a special case. Both analytical and numerical solutions are presented for momentum and energy boundary layer equations by using the similarity transformation and shooting technique and the associated transfer characteristics are discussed.     

Study of transition from laminar to turbulent boundary layer on a tilted flat plate using heat transfer measurements

The boundary layer transition over a flat tilted plate has been studied by means of heat transfer measurements.Aheat flux sensor has been developed,in order to measure the efficiency of convective heat transfer for varioustypes of surfaces or flows.Its operation at constant temperature allows direct and fast measurements of heat flux.The present paper reports the development of the sensor and presents its application to the study of transition in aboundary layer depending on the angle of incidence of the external flow.An exponential relationship betweencritical Reynolds number and pressure gradient parameter has been found.     

幂律流体连续运动平板边界层的数值研究

利用数值模拟方法研究了幂律流体在连续运动平板上的层流边界层问题。利用相似变换理论推导出无量纲剪切力的计算公式,数值求解了不同幂律指数n的流体在不同运动参数ξ的连续运动平板上的层流边界层流场,分析了各个参数对边界层速度分布和剪切力大小的影响。结果表明,边界层偏微分方程组的数值解与经过相似变换求得的非线性常微分方程的数值解吻合得很好,这既说明对幂律流体连续运动平板上的层流边界层问题的研究是有效且可靠的,同时也证明了连续运动平板问题存在相似解。     

Effect of boundary layer trip on reduction of jet noise in over-expanded nozzle flow

A flow resonance accompanied by the emission of acoustic tones occurs in an over-expanded convergent-divergent (C-D) nozzle when operated at comparatively low pressure ratios.This phenomenon is distinguished from conventional screech tones and is referred to as “transonic tones”.In contrast to screech tones,the peak resonant frequency for transonic tones increases with pressure ratio;the peak sound pressure level exceeds 110 dB.In this study,we investigated the basic characteristics of transonic resonance and tones using a circular C-D nozzle in an anechoic room.The effects of the boundary layer trip were also evaluated using a tripping wire for the suppressing transonic resonance and tones.The results of acoustic measurements show that several predominant peaks correspond to transonic tones.However,the boundary layer trip inside the nozzle effectively eliminated these tones and suppressed the unsteadiness of the flow inside the nozzle.     

Heat transfer in a forced wall jet on a heated rough surface

Many stUdies of wall Jets on smooth, flat and curveds~es haVe been examined over the past fifty years.Glauertll] realized the first comprehensive study of thewall jet. A survey by Launder and Rodiln summarizedmost of the known results on tulbulent jet flows on flatsauce. The stUdy of the effect of significant rouglmesscaused by the deposition of pericles on a heated wallsubmited tO acoustic vibrations, can be interesting foraPPlications in problems of cooling in engine brineblades, for exa…     

Nonsimilar boundary layer flow of Cross fluid induced by a heated stretched sheet

This paper deals with the nonisothermal boundary layer flow of Cross fluid due to a stretching sheet. Unlike previous studies on boundary layer flow of Cross fluid, a nonsimilar formulation is adopted to transform the boundary layer equations into nondimensional form. The problem is characterized by three dimensionless parameters, namely, the Deborah number, the Prandtl number, and dimensionless distance along the sheet. The transformed equations are simulated by a numerical scheme with the help of MAPLE software. The velocity and temperature profiles inside the boundary layer are calculated and shown graphically. The skin friction coefficient and Nusselt number at various axial stations are also tabulated for several values of Deborah number and Prandtl number.     

Skin friction and heat transfer in power-law fluid laminar boundary layer along a moving surface

Analytical and numerical solutions are presented for momentum and energy laminar boundary layer along a moving plate in power-law fluids utilizing a similarity transformation and shooting technique. The results indicate that for a given power-law exponent n(0<n?1) or velocity ratio parameter ξ, the skin friction σ decreases with the increasing in ξ or n. The shear force decreases with the increasing in dimensionless tangential velocity t. When Prandtl number N_Pr=1, the dimensionless temperature w(t) is a linear function of t, and the viscous boundary layer is similar to that of thermal boundary layer. In particular, w(t)=t if ξ=0, i.e., the velocity distribution in viscous boundary layer has the same pattern as the temperature distribution in the thermal boundary and δ=δ_T. For N_Pr?1, the increase of viscous diffusion is larger than that of thermal diffusion with the increasing in N_Pr, and δ_T(t)<δ(t). The thermal diffusion ratio increases with the increasing in n(0<n?1) and ξ.     

Conjugate forced convection heat transfer from a flat plate by laminar plane wall jet flow

An analytical solution is investigated for forced convection heat transfer from a laminar plane wall jet as conjugate case. For Re ? 1, boundary layer theory is used for the investigation. The problem has been solved for two classic cases such as Pr ? 1 and Pr ? 1. The conjugate model consists of considering the full Navier-Stokes equation in the fluid medium and coupling of energy equations in the fluid and the slab through the interface boundary conditions. Closed-form relations are found for Nusselt number (Nu), average Nusselt number and conjugate interface boundary temperature (θ_b). The effects of the Reynolds number (Re), the Prandtl number (Pr), the thermal conductivity ratio (k) between the slab and the fluid medium and the slab aspect ratio (λ) are investigated on the heat transfer characteristics. The analytical results are compared with the full numerical results.     

Natural convection boundary layer flow of nanofluids around different stations of the sphere and into the plume above the sphere

The main intent of the present study is to investigate the natural convection boundary layer flow of nanofluids around different stations of the sphere and eruption of the fluid from the boundary layer in to the plume above the sphere. It is pertinent to point out that in this study heated sphere is treated as point source. The system of transport boundary layer equations is based on the effects of Brownian motion and thermophoresis. The system of dimensioned boundary layer equations is transformed into nondimensional form. Later, the nondimensional form of the mathematical model is solved numerically by using implicit finite difference method. The solution of the problem depends on a controlling parameters Prandtl number P_r, Lewis number , thermophoresis parameter , and Brownian motion parameter . Particularly, it is observed that for Lewis number , Prandtl number P_r, Brownian motion parameter , and thermophoresis parameter the velocity profile is maximum at station and minimum at station . On the other hand temperature distribution is uniform at each station around the sphere and slightly reduced for . It is also observed that nanoparticles concentration is maximum at station and minimum at station We also established the result that with the increase of skin friction is reduced while the heat and mass flux are increased in the plume region‐III.     

Numerical analysis of the effect of boundary layer thickness on vortex structures and heat transfer in the wake behind a hill

This study presents a three‐dimensional numerical analysis of the effect of boundary layer thickness on vortex structures and heat transfer behind a hill mounted in a laminar boundary layer. When the thickness of the velocity boundary layer is comparable to the hill height, a hairpin vortex is formed symmetrically to the center of the spanwise direction in the wake. A secondary vortex is formed between the legs, and horn‐shaped secondary vortices appear under the concave parts of the hairpin vortex. When the boundary layer thickness increases, the legs and horn‐shaped secondary vortices move toward the center of the spanwise direction, and thus heat transport and heat transfer increase there. At this time, high‐turbulence areas generated locally move toward the center of the spanwise direction with an increase in the boundary layer thickness. With a further increase in the boundary layer thickness, steady streamwise vortices are formed downstream of the hill, but the heat transfer decreases. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20261     

Large eddy simulation of reacting flow in a hydrogen jet into supersonic cross-flow combustor with an inlet compression ramp

Large eddy simulation (LES) has been performed to investigate transverse hydrogen jet mixing and combustion process in a scramjet combustor model with a compression ramp at inlet to generate shock train. Partially Stirred Reactor (PaSR) sub-grid combustion model with a skeleton of 19 reactions and 9 species hydrogen/air reaction mechanism was used. The numerical solver is implemented in an Open Source Field Operation and Manipulation (OpenFOAM) and validated against experimental data in terms of mean wall pressure. Effects of a shock train induced by the inlet compression ramp on the flame stabilization process are then studied. It can be observed that the interaction of the oblique shock and the jet mixing layer enhance the combustion and stabilize the flame. Symmetrical recirculation zone, which contributes to the flame anchoring of the supersonic transverse jet combustion, is observed in the near wall region of 10 < x/D < 20. The hydrogen fuel is transported from the center of jet plume to the near wall region on both sides of the central plane (z/D = 0) and thus intense combustion near the wall is observed due to the enhanced mixing and shock compression heating. Besides, the jet penetration in the reacting field is different from that in non-reacting case with the influence of the interaction between the reflected oblique shock and the jet shear layer on the windward side.     

Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid

This work studies the free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar governing equations are then solved by the cubic spline collocation method. The effects of the Brownian motion parameter and thermophoresis parameter on the profiles of the temperature, nanoparticle volume fraction and velocity profiles are presented. The local Nusselt number is presented as a function of the thermophoresis parameter, Brownian parameter, Lewis number and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). Results show that the local Nusselt number is increased as the thermophoresis parameter or the Brownian parameter is decreased. The local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased. Moreover, the local Nusselt number of the elliptical cylinder with slender orientation is higher than those of the elliptical cylinder with blunt orientation over the lower half cylinder.