Thermal-drag and Transition from Quasi-steady to Highly-unsteady Combustion of a Fuel Droplet in the Presence of Upstream Velocity Oscillations

Numerical studies on the behaviors of combustion of 1-butanol fuel droplet at presence of upstream velocity oscillation are performed. Fuel droplet has an initial diameter of 1.25 mm and ambiance pressure and temperature are 0.4 MPa and 300 K, respectively. These conditions are those in which the microgravity experiments in literature conducted. In the excellent agreement with the experimental data, numerical results show a significant enhancement of the burning rate of droplet compared to what is predicted by quasi-steady film theory models. The mechanism of the enhancement of burning rate is clarified then by observation of a new mechanism that is named thermal-drag, TD. It is shown, depending on the amplitude and frequency of the upstream velocity oscillation, the flame in wake region of droplet can move toward the droplet surface by the force of vortex flow motions produced by the TD mechanism. It is verified that such movement of the flame is responsible for the enhancement of the burning rate and deviation of the response of the evaporation process form the predictions of the quasi-steady model. Frequency analysis of the burning rate reveals that at low frequency and amplitude the FFT diagram of the burning rate contains of only one main peak synchronies with the frequency of upstream velocity oscillation, which implies a quasi-steady response. However; at high frequency and amplitude the diagram includes of wide range of frequencies beside of the main peak that readily shows deviation from the quasi-steady conditions. In the latter, the study on the response of the combustion to the upstream velocity fluctuations in which the fluctuations contains of three wave numbers shows the amplification of the effects of low frequency fluctuations rather than that of damping of the effects of high frequency fluctuations on the evaporation processes.     

The influence of thermal expansion flow on droplet evaporation

It has been demonstrated recently that it follows from conservation of mass that unsteady temperature fields create flow in an incompressible fluid with a temperature-dependent density even in the absence of gravity. The paper studies the influence of thermal expansion flow on spherically symmetric evaporation of an isolated droplet. A model problem of a droplet evaporating at a constant rate is first considered. In this idealized situation one can use the assumption of a thin thermal boundary layer to solve analytically the unsteady moving-boundary heat conduction problem to find the temperature field inside the droplet both with and without the thermal expansion flow. Next evaporation of a fuel droplet in a diesel engine is studied numerically. The heat diffusion equation is solved in the liquid phase while the standard quasi-steady model is used for the gas phase. The results of the calculation show that for high ambient temperatures the influence of the thermal expansion flow on the droplet lifetime can be considerable.     

Numerical simulation and experimental study of heat and mass transfer in fuel droplet evaporation

Heat and mass transfer in fuel droplet evaporation are investigated through numerical simulation and experimental study. The effect of liquid-phase heat transfer is studied using the temperature difference between the gas- and liquid-phase droplets, different turbulent intensity and oscillatory flow frequency. For the two-droplet array, some differences in heat and mass transfer mechanisms are found. For different spacing of the two-droplet array, the downstream droplet evaporation is affected by the lead droplet.     

Evaporation phenomenon past a rotating hydrocarbon droplet of ternary components

A numerical study of heat and mass transfer from an evaporating fuel droplet rotating around its vertical axis was performed in forced convection only on the side opposite to the flow. The flow was assumed to be laminar, and the droplet was assumed to maintain its spherical shape during its lifetime. Based on the abovementioned assumption, the conservation equations in a general curvilinear coordinate were solved numerically. The behavior of rotating droplet evaporation in the forced convection flow can be investigated by analyzing the effects of the rotation of the droplet on the evaporation process of multi-component hydrocarbons droplet. The droplet is simulated to behave as a hard sphere. The transfer equations are discretized using an implicit finite difference method. Thomas algorithm is used to solve the system of algebraic equations. Moreover, dimensionless parameters of heat and mass transfer phenomena around a rotating hydrocarbon droplet were determined. The thickness of the boundary layer is unknown for this model and therefore, it was determined in function of time. Additionally, the study concerns “Dgheim dimensionless number” which is the ratio of the rotation forces over the viscosity forces. Dgheim dimensionless number is correlated to Nusselt and Sherwood numbers for multi-component hydrocarbon droplets in evaporation by taking into account the effect of heat and mass Spalding, Prandtl and Schmidt numbers respectively. Also, correlations for Nusselt and Sherwood numbers in terms of Reynolds, Prandtl and Schmidt numbers are proposed. These correlations consider the rotation phenomenon and advance the variation of the thermophysical and transport properties in the vapor phase of multi-component blends.     

Numerical Investigation of Unsteady Transitional Flows in Turbomachinery Components Based on a RANS Approach

This paper presents results of the numerical simulation of periodically unsteady flows with focus on turbomachinery applications. The unsteady CFD solver used for the simulations is based on the Reynolds averaged Navier–Stokes equations. The numerical scheme applies an extended version of the Spalart–Allmaras one-equation turbulence model coupled with a transition correlation. The first example of validation consists of boundary layer flow with separation bubble on a flat plate, both under steady and periodically unsteady main flow conditions. The investigation includes a variation of the major parameters Strouhal number, amplitude, and Reynolds number. The second, more complex test case consists of the flow through a cascade of turbine blades which is influenced by wakes periodically passing over the cascade. The computations were carried out for two different blade loadings. The results of the numerical simulations are discussed and compared with experimental data in detail. Special emphasis is given to the investigation of boundary layers with regard to transition, separation and reattachment under the influence of main flow unsteadiness. This revised version was published online in July 2006 with corrections to the Cover Date.     

Unsteady effects in mechanically-excited turbulent plane jets

Two methods of mechanically exciting a plane turbulent free jet are described; periodic perturbatin of the nozzle exit velocity, and forced oscillation of a small vane located in the het potential core. Hot-wire measurements obtained by conditional sampling techniques indicated that the flow fields of the two jets are substantially different although they have the same Strouhal number of 0.0032. While the mean flow development of the pulsed jet can be described adequately by a quasi-steady model, the vane-excited jet exhibits unsteady effects which depart significantly from quasi-steady approximations such as increased entrainment, amplification of excitation and non-linear effects in the form of the presence of high harmonics. The constancy of momentum flux has been examined in both the steady and unsteady jets     

The unsteady drag on a spherical bubble at large Reynolds numbers

The flow past a spherical bubble undergoing a rectilinear motion in the unsteady flow of an unbounded liquid medium is investigated. The liquid velocity field at infinity is assumed to be uniform and the Reynolds number to be large. The Strouhal number is taken to be of order unity. The velocity distribution is sought by superposition of a perturbation field on the potential flow past the bubble so that the flow field is divided into four regions, i.e. the external flow field where the potential flow holds, the boundary layer, the rear stagnation point region and the wake. The flow in the rear stagnation point region and the wake is assumed to be essentially inertial. The unsteady drag experienced by the bubble is calculated from the mechanical energy balance of the liquid.     

Numerical simulation of shear effect on vortex shedding behind a square cylinder

This paper is concerned with the numerical simulation of the flow structure around a square cylinder in a uniform shear flow. The calculations were conducted by solving the unsteady 2D Navier–Stokes equations with a finite difference method. The effect of the shear parameter K of the approaching flow on the vortex-shedding Strouhal number and the force coefficients acting on the square cylinder is investigated in the range K=0·0–0·25 at various Reynolds numbers from 500 to 1500. The computational results are compared with some existing experimental data and previous studies. The effect of shear rate on the Strouhal number and the force acting on the cylinder has a tendency to reduce the oscillation. The Strouhal number, mean drag and amplitude of the fluctuating force tend to decrease as the shear rate increases, but show no significant change at low shear rate. Increasing the Reynolds number decreases the Strouhal number and increases the force acting on the cylinder. At high shear rate the shedding frequencies of the fluctuating drag and lift coefficients are identical. © 1997 John Wiley & Sons, Ltd.     

Prediction of periodic boundary layers

A relatively simple, yet efficient and accurate finite difference method is developed for the solution of the unsteady boundary layer equations for both laminar and turbulent flows. The numerical procedure is subjected to rigorous validation tests in the laminar case, comparing its predictions with exact analytical solutions, asymptotic solutions, and/or experimental results. Calculations of periodic laminar boundary layers are performed from low to very high oscillation frequencies, for small and large amplitudes, for zero as well as adverse time-mean pressure gradients, and even in the presence of significant flow reversal. The numerical method is then applied to predict a relatively simple experimental periodic turbulent boundary layer, using two well-known quasi-steady closure models. The predictions are shown to be in good agreement with the measurements, thereby demonstrating the suitability of the present numerical scheme for handling periodic turbulent boundary layers. The method is thus a useful tool for the further development of turbulence models for more complex unsteady flows.     

Numerical investigation of confined wakes behind a square cylinder in a channel

The structure of confined wakes behind a square cylinder in a channel is investigated via the numerical solution of the unsteady Navier–Stokes equations. Vortex shedding behind the cylinder induces periodicity in the flow field. Details of the phenomenon are simulated through numerical flow visualization. The unsteady periodic wake can be characterized by the Strouhal number, which varies with the Reynolds number and the blockage ratio of the channel. The periodicity of the flow is, however, damped in the downstream region of a long duct. This damping may be attributed to the influence of side walls on the flow structure.     

Velocity measurements of wake-induced unsteady flow in a linear turbine cascade

Extensive velocity measurements have been taken in a linear turbine cascade with unsteady oncoming wakes. The unsteady wakes were generated by moving cylinders on a squirrel cage device. The Reynolds number was 1.1 × 10⁵, and the Strouhal number varied from o to 7.36. The blade-to-blade flow and the boundary layers on the suction side were measured with a hot-wire anemometer. The results were obtained in ensemble-averaged form so that periodic unsteady processes can be studied. Of particular interest was the transition of the boundary layer. The boundary layer remained laminar in the case without wakes. The passing wakes caused transition, and the beginning of transition moves forward as the wake-passing frequency increases. Unlike in the flat plate study of Liu and Rodi (1991a) the boundary layer state hardly changed with time, although the turbulence level in the boundary layer showed clear periodic response to the passing wakes. The work reported here was sponsored by the German Federal Ministry of Research and Technology through program TURBOTHERM under contract no. 0326501D. The authors should like to thank Mr. D. Bierwirth for his excellent technician work on this project, Dr. N. H. Cho for his help with the preparation of the plots and Mrs. R. Zschernitz for her expert typing of the text.     

Unsteady MHD free convection flow past a vertical permeable flat plate in a rotating frame of reference with constant heat source in a nanofluid

The unsteady magnetohydrodynamic flow of a nanofluid past an oscillatory moving vertical permeable semi-infinite flat plate with constant heat source in a rotating frame of reference is theoretically investigated. The velocity along the plate (slip velocity) is assumed to oscillate on time with a constant frequency. The analytical solutions of the boundary layer equations are assumed of oscillatory type and they are obtained by using the small perturbation approximations. The influence of various relevant physical characteristics are presented and discussed.     

Shock wave induced evaporation of water droplets in a gas-droplet mixture

A model is presented for the droplet evaporation process induced by a shock wave propagating in a fog. The model is based on the existence of a quasi-steady wet bulb state of the droplets during evaporation. It is shown that for moderate shock strength, Ma = < 2, and droplet radii in the range of 1–5 the, the major part of the evaporation process is governed by a balance between heat conduction and vapour diffusion. The formation of a fog by means of an unsteady adiabatic expansion of humid nitrogen is described. Experimental results of shock induced evaporation are shown for shock Mach numbers from 1.2 to 2.1, droplet mass fraction of 5 · 10^-3, and initial droplet radii of 1–1.4 m. The expected linear relation between droplet radius squared and time during evaporation is observed. Characteristic evaporation times appear to be strongly dependent on shock strength. A variation of about two decades, predicted by theory, was experimentally observed for the Mach number range studied.     

Hydrodynamics of a tandem fish school with asynchronous undulation of individuals

We perform numerical simulations using immersed boundary method for flow over a single and two fish in tandem performing traveling wave like motion for a range of Strouhal numbers. We investigate the hydrodynamic performance of single- and tandem-fish configurations using unsteady profiles of lateral side-force and drag coefficients, their time-averaged values, and wake behind these bodies. We present the spectra of hydrodynamic forces and find that the nature of these forces for a single fish resembles to those of stationary/oscillating bluff bodies and oscillating airfoils. For tandem cases, we vary the phase speed of undulatory motion of the rear fish while keeping the free-stream velocity constant. We show that hydrodynamic forces of the upstream and rear fish contain harmonics which are produced by nonlinear interaction of the oscillation frequencies of both fish. We find that the wake and time-averaged drag of the upstream fish remain almost independent of the undulating frequency of the rear fish at a certain Strouhal number. We also relate this observation with the absence of oscillation frequency of the rear fish in the Fourier spectra of hydrodynamic forces of the upstream fish. For the complete range of parameters, it is inferred that swimming in a tandem configuration seems more beneficial for the upstream fish. It happens due to wake-splitting effect of the rear fish that causes an enhancement of pressure in its wake. For the rear fish, it gains an advantage of drafting under certain conditions and its performance deteriorates at Strouhal numbers greater than 0.40.     

Unsteady laminar flow developing in a curved duct

The flow developing in a tightly curved U-bend of square cross section has been investigated experimentally and via numerical simulation. Both long-time averages and time histories of the longitudinal (streamwise) component of velocity were measured using a laser-Doppler velocimeter. The Reynolds number investigated was Re = 1400. The data were obtained at different bend angles, θ, and were confined to the symmetry plane of the bend. At Re = 1400, the flow entering the bend is steady, but by θ = 90° it develops an oscillatory component of motion along the outer-radius wall. Autocorrelations and energy spectra derived from the time histories yield a base frequency of approximately 0.1 Hz for these oscillations. Flow-visualization studies showed that the proximity of the outer-radius wall served to damp the amplitude of the spanwise oscillations.

Numerical simulations of the flow were performed using both steady and unsteady version of the finite-difference elliptic calculation procedure of Humphrey et al. (1977). Although the unsteadiness observed experimentally does not arise spontaneously in the calculations, numerical experiments involving the imposition of a periodic time-dependent perturbation at the inlet plane suggest that the U-bend acts upon the incoming flow so as to damp the amplitude of the imposed oscillation while altering its frequency.

The oscillations observed experimentally, and numerically as a result of the periodic perturbation, have been linked to the formation of Goertler-type vortices of the outer-radius wall in the developing flow. The vortices, which develop as a result of the centrifugal instability of the flow on the outer-radius wall, undergo a further transition to an unsteady regime at higher flow rates.     

Mass transfer characteristics in an axisymmetric wavy-walled tube for pulsatile flow with backward flow

Under the pulsatile flow with backward flow (PFBF) conditions, flow mixing and mass transfer characteristics are experimentally investigated in an axisymmetric wavy-walled tube at a net flow Reynolds number from 50 to 1,000. An electrochemical technique is employed to measure the mass transfer rate. An optimal Strouhal number corresponding to the peak value of the mass transfer enhancement factor is observed, which is independent of the oscillatory fraction of the flow rate, but decreases with the increasing net flow Reynolds number. It was found that the mass transfer enhancement under PFBF has the similar characters of resonant enhancement in two-dimensional (2-D) channels, but there also exists an essential difference since no self-sustained oscillation occurs in the wavy-walled tube.     

煤油液滴直径对两相旋转爆轰发动机流场的影响

为探究煤油液滴不同初始直径对气液两相旋转爆轰发动机流场的影响,假设初始注入的煤油液滴具有均匀直径,考虑雾化破碎、蒸发等过程,建立了非定常两相爆轰的Eulerian-Lagrangian模型,进行了液态煤油/高温空气爆轰的非预混二维数值模拟。结果表明：在初始液滴直径为1～70μm的工况范围,燃烧室内均形成了单个稳定传播的旋转爆轰波;全局当量比为1时,爆轰波前的空气区域大于液滴煤油的蒸气区域,导致波前燃料空气混合不均匀,波前均存在富油区和贫油区,两相速度差导致分离出的空气形成低温条带;当煤油液滴的初始直径较小时,波前的反应物混合过程主要受蒸发的影响,爆轰波可稳定传播;当直径减小至1μm时,煤油液滴在入口处即蒸发,旋转爆轰波表现为气相传播的特性,爆轰波结构平整;当煤油液滴的初始直径较大时,波前的反应物混合过程主要受液滴破碎的影响;对于相同的燃料质量流量,在不同初始煤油液滴直径工况下,煤油液滴最大的停留时间均占爆轰波传播时间尺度的80%以上;爆轰波前燃料预蒸发为气相的占比越高,爆轰波的传播速度越高;初始液滴直径为10～70μm的工况范围内,爆轰波的速度随初始直径的增大先升高后降低。     

Transition mechanisms in laminar separation bubbles with and without incoming wakes and synthetic jet effects

Laminar separation and transition processes of the boundary layer developing under a strong adverse pressure gradient, typical of Ultra-High-Lift turbine profiles, have been experimentally investigated for a low Reynolds number case. The boundary layer development has been surveyed for different conditions: with steady inflow, with incoming wakes and with the synchronized forcing effects due to both incoming wakes and synthetic jet (zero net mass flow rate jet). In this latter case, the jet Strouhal number has been set equal to half the wake-reduced frequency to synchronize the unsteady forcing effects on the boundary layer. Measurements have been taken by means of a single-sensor hot-wire anemometer. For the steady inflow case, particle image velocimetry has been employed to visualize the large-scale vortical structures shed as a consequence of the Kelvin?CHelmholtz instability mechanism. For the unsteady inflow cases, a phase-locked ensemble averaging technique, synchronized with the wake and the synthetic jet frequencies, has been adopted to reconstruct the boundary layer space-time evolution. Results have been represented as color plots, for several time instants of the forcing effect period, in order to provide an overall view of the time-dependent transition and separation processes in terms of ensemble-averaged velocity and unresolved unsteadiness distributions. The phase-locked distributions of the unresolved unsteadiness allowed the identification of the instability mechanisms driving transition as well as the Kelvin?CHelmholtz structures that grow within the separated shear layer during the incoming wake interval and the synthetic jet operating period. Incoming wakes and synthetic jet effects in reducing and/or suppressing flow separation are investigated in depth.