Large eddy simulation of vertical turbulent jets under JONSWAP waves

The effect of random waves on vertical plane turbulent jets is studied numerically and the mechanism behind the interaction of the jet and waves is analyzed. The large eddy simulation method is used and the σ-coordinate system is adopted. Turbulence is modeled by a dynamic coherent eddy model. The σ-coordinate transformation is introduced to map the irregular physical domain with a wavy free surface and an uneven bottom onto a regular computational domain. The fractional step method is used to solve the fil...     

Particle removal from a surface by a bounded vortex flow

A bounded vortex flow consists of an axisymmetric vortex that is confined top and bottom between two plates (the “confinement plate” and “impingement plate”, respectively) and surrounded laterally by a swirling annular slot jet. The bottom of the vortex terminates on the boundary layer along the impingement plate and the top of the vortex is drawn into a suction port positioned at the center of the confinement plate. The circumferential flow within the annular jet is important for supplying circulation to the central wall-normal vortex. This flow field is proposed as a method for mitigation of dust build-up on a surface, where the vortex–jet combination supplements the more traditional vacuum port by enhancing the surface shear stress and related particle transport rate. The paper reports on a computational study of the velocity field and particle transport by a bounded vortex flow. Fluid flow computations are performed using a finite-volume approach for an incompressible fluid and particle transport is simulated using a discrete-element method. Computations are performed for different values of two dimensionless parameters – the ratio of the plate separation distance and the average radial location of the jet inlet (the dimensionless confinement height) and the ratio of flow rate withdrawn at the suction outlet and that injected by the jet (the flow rate ratio). For small values of the flow rate ratio, the impinging jet streamlines pass down to the boundary layer along the bottom surface and then travel up the vortex core. By contrast, for large values of flow rate ratio, the annular jet is quickly entrained into the suction outlet and no wall-normal vortex is formed. Particles are observed to roll along the impingement surface in a direction determined by the fluid shear stress lines. Particles roll outward when they lie beyond a separatrix curve of the surface shear stress lines, where particles within this separatrix curve roll inward, piling up at the center of the flow field. A toroidal vortex ring forms for the small confinement height case with flow rate ratio equal to unity, which yields double separatrix curves in the shear stress lines. The inward rolling particles intermittently lift up due to collision forces and burst away from the impingement surface, eventually to become entrained into the flow out the suction port or resettling back onto the impingement surface.     

Unsteady shrinking sheet with mass transfer in a rotating fluid

In this paper, the problem of unsteady flow induced by a shrinking sheet with mass transfer in a rotating fluid is studied. The transformed boundary layer equations are solved numerically by an implicit finite‐difference scheme known as the Keller‐box method. The influence of rotation, unsteadiness and mass suction parameters on the reduced skin friction coefficients f″(0) and g′(0), as well as the lateral velocity and velocity profiles are presented and discussed in detail. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical modeling of multi micro jet impingement cooling of a three dimensional turbine vane

This paper reports a numerical investigation on the prediction of the thermal and hydrodynamic flow fields of multi micro jet impingement cooling of three dimensional turbine vanes. A three dimensional vane is modeled with an in-line array of impinging jets of diameters 0.5 and 0.25 mm. The numerical model consists of the steady, Reynolds-Averaged Navier–Stokes equations and the Kω SST Turbulence model. The governing equations are solved using a finite volume method. The crossflow mass velocity (G _c ) to jet mass velocity (G _j ) ratio, and the average and local heat transfer distributions are analyzed with varying mass velocity and jet-to-target spacing. It is found out that a significant decrease in crossflow ratio occurs with the smaller diameters. Due to the lower crossflow and higher exit velocities of the smaller jets, the penetration into the crossflow is much higher. Moreover, at a constant mass flow, the use of micro-jets enhanced the overall average heat transfer coefficient by 63%, while at a fixed pressure drop across the vane instead of the mass flow, the smaller diameters will still yield an enhancement of 34.3% in the overall average heat transfer coefficient.     

Computations for a jet impinging obliquely on a flat surface

A SIMPLE-C algorithm and Jones-Launder k-ε two-equation turbulence model are used to simulate a two-dimensional jet impinging obliquely on a flat surface. Both the continuity and momentum equations for the unsteady state are cast into suitable finite difference equations. The pressure, velocity, turbulent kinetic energy and turbulent energy dissipation rate distributions are solved and show good agreement with various experimental data. The calculations show that the flow field structure of the jet impinging obliquely on a flat surface is strongly affected by the oblique impingement angle. The maximum pressure zone of the obliquely impinging jet flow field moves towards the left as the oblique impingement angle is decreased.     

Flow analysis of two-dimensional pulsed jets by particle image velocimetry

A purely alternating jet without mean mass flux and a mixed pulsed jet containing an additional blowing component were investigated by particle image velocimetry (PIV). The jets issued from a two-dimensional slit connected to a converging nozzle, opening normally from a flat wall. The pulsation was driven by a loudspeaker. The mean velocity fields were characterized by the combination of downstream directional blowing and omni-directional suction. The velocity fluctuations were dominated by contra-rotating eddy pairs synchronized with the pulsation and formed at the jet edges during blowing. Phase-synchronized measurements permit the investigation of the averaged patterns and the cycle-to-cycle fluctuations of these vortices. The mean trajectories of vortex centers during a whole injection cycle show how large lateral jet expansions are achieved. For a purely alternating jet, the expansion takes place close to the slit. For a mixed pulsed jet, the vortices develop farther from the orifice. In addition, proper orthogonal mode decomposition demonstrates that only a few modes are required to represent the main events of the flow dynamics. Received: 10 August 1999 / Accepted: 10 January 2001     

Effect of jet-to-plate spacing in laminar array jets impinging

The rate of heat transfer from a plate due to impinging of an array of jets was investigated. The effect of jet-to-plate spacing in a confined array of impinging laminar square jets was investigated numerically through the solution of Navier Stokes and energy equations. The simulation is carried out for the jet-to-plate spacing between 2 B and 20 B and for jet-to-jet spacing of 4 B, where B is the jet width. Five in-line jets subjected to across-flow were used in this investigation. Also, six different ratios of jet to cross-flow velocity are simulated (0.5, 1.0, 2.5, 5, 7.5 and 10) for the jet Reynolds number of 200. The predicted results show a formation of one or two ground horseshoe vortices between the jets. In addition, a horseshoe vortex forms at different position between the orifice and impinging plates due to the interaction of two jets before they combine. The number of the ground horseshoe vortex and its size are strongly affected by the jet-to-plate spacing and by jet to cross-flow velocity ratio. The effect of jet-to-plate spacing and jet to cross-flow velocity ratio on heat transfer is presented and discussed.     

Flow of a viscous incompressible fluid of temperature dependent viscosity past a permeable wedge with uniform surface heat flux

 The effect of uniform suction on the steady two-dimensional laminar forced flow of a viscous incompressible fluid of temperature dependent viscosity past a wedge with uniform surface heat flux is considered. The governing equations for the flow are obtained by using suitable transformations and are solved by using an implicit finite difference method. Perturbation solutions are also obtained near the leading edge and in the downstream regime. The results are obtained in terms of the local skin friction coefficient and the rate of heat transfer for various values of the pertinent parameters, such as the Prandtl number, Pr, the velocity gradient parameter, m, the local suction parameter, ξ, and the viscosity variation parameter, ɛ. Perturbation solutions are compared with the finite difference solutions and are found to be in excellent agreement. The effect of ξ, m and ɛ on the dimensionless velocity profiles and viscosity distribution are also presented graphically for Pr = 0.7 and 7.0, which are the appropriate values for gases and water respectively. Received on 22 July 1999     

Axisymmetric stagnation flow obliquely impinging on a moving circular cylinder with uniform transpiration

Laminar stagnation flow, axisymmetrically yet obliquely impinging on a moving circular cylinder, is formulated as an exact solution of the Navier–Stokes equations. Axial velocity is time‐dependent, whereas the surface transpiration is uniform and steady. The impinging free stream is steady with a strain rate k?. The governing parameters are the stagnation‐flow Reynolds number Re=k?a²/2ν, and the dimensionless transpiration S=U₀/k?a. An exact solution is obtained by reducing the Navier–Stokes equations to a system of differential equations governed by Reynolds number and the dimensionless wall transpiration rate, S. The system of Boundary Value Problems is then solved by the shooting method and by deploying a finite difference scheme as a semi‐similar solution. The results are presented for velocity similarity functions, axial shear stress and stream functions for a variety of cases. Shear stresses in all cases increase with the increase in Reynolds number and suction rate. The effect of different parameters on the deflection of viscous stagnation circle is also determined. Copyright © 2010 John Wiley & Sons, Ltd.     

Large-eddy Simulation of Film Cooling Flows with Variable Density Jets

The present paper investigates the impact of the velocity and density ratio on the turbulent mixing process in gas turbine blade film cooling. A cooling fluid is injected from an inclined pipe at α=30° into a turbulent boundary layer profile at a freestream Reynolds number of Re_∞ = 400,000. This jet-in-a-crossflow (JICF) problem is investigated using large-eddy simulations (LES). The governing equations comprise the Navier–Stokes equations plus additional transport equations for several species to simulate a non-reacting gas mixture. A variation of the density ratio is simulated by the heat-mass transfer analogy, i.e., gases of different density are effused into an air crossflow at a constant temperature. An efficient large-eddy simulation method for low subsonic flows based on an implicit dual time-stepping scheme combined with low Mach number preconditioning is applied. The numerical results and experimental velocity data measured using two-component particle-image velocimetry (PIV) are in excellent agreement. The results show the dynamics of the flow field in the vicinity of the jet hole, i.e., the recirculation region and the inclination of the shear layers, to be mainly determined by the velocity ratio. However, evaluating the cooling efficiency downstream of the jet hole the mass flux ratio proves to be the dominant similarity parameter, i.e., the density ratio between the fluids and the velocity ratio have to be considered.     

Unsteady flow and heat transfer past an axisymmetric permeable shrinking sheet with radiation effect

In this paper, the problem of unsteady axisymmetric boundary layer flow and heat transfer induced by a permeable shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by an implicit finite‐difference scheme known as the Keller‐box method. The influence of radiation, unsteadiness and mass suction parameters on the reduced skin friction coefficient f′′(0) and the heat transfer coefficient ?θ′(0), as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and suction parameter delays the separation of boundary layer. Copyright © 2010 John Wiley & Sons, Ltd.     

On unsteady flow of an elastico-viscous fluid past an infinite plate with variable suction

Approximate solutions of the Navier-Stokes equations are derived through the Laplace transform for two dimensional, incompressible, elastico-viscous flow past a flat porous plate. The flow is assumed to be independent of the distance parallel to the plate. General formulae for the velocity distribution, skin friction and displacement thickness as functions of the given free stream velocity and suction velocity are obtained. The response of skin friction to the impulsive perturbations in the stream and suction velocities is studied. It is found that the order of singularity in the skin friction at t=0 increases due to the elastic property of the fluid in the impulsive case. When the stream is accelerated the skin friction still anticipates the velocity but the time of anticipation is reduced from 1/4 to (1/4) (1—k), where k is the elastic parameter of the fluid. It is found that in general the resistance of the elastico-viscous fluids to an impulsive increase in the stream velocity is greater than the viscous fluids, the elasticoviscous fluids also reach the steady state earlier than the viscous fluids.     

Nonsimilar boundary-layer flow over a stationary permeable plate in a rotating fluid with a magnetic field

Summary  The nonsimilar boundary-layer flow and heat transfer over a stationary permeable surface in a rotating fluid in the presence of magnetic field, mass transfer and free stream velocity are studied. The parabolic partial differential equations governing the flow have been solved numerically by using a difference–differential method. For small streamwise distance, these partial differential equations are also solved by a perturbation technique with Shanks transformation. For uniform mass transfer, analytical solutions are obtained. The surface skin friction coefficients and the Nusselt number increase with the magnetic field, suction and streamwise distance from the leading edge of the plate except the skin friction coefficient in the y-direction which decreases with the increasing magnetic field. Received 4 December 2001; accepted for publication 24 September 2002     

Numerical simulation of turbulent impinging jet on a rotating disk

The calculations of quasi‐three‐dimensional momentum equations were carried out to study the influence of wall rotation on the characteristics of an impinging jet. The pressure coefficient, the mean velocity distributions and the components of Reynolds stress are calculated. The flow is assumed to be steady, incompressible and turbulent. The finite volume scheme is used to solve the continuity equation, momentum equations and k–ε model equations. The flow characteristics were studied by varying rotation speed ω for 0?ω?167.6 rad/s, the distance from nozzle to disk (H/d) was (3, 5, 8 and 10) and the Reynolds number Re base on V_J and d was 1.45 × 10⁴. The results showed that, the radial velocity and turbulence intensity increase by increasing the rotation speed and decrease in the impingement zone as nozzle to disk spacing increases. When the centrifugal force increases, the radial normal stresses and shear stresses increase. The location of maximum radial velocity decreases as the local velocity ratio (α) increases. The pressure coefficient depends on the centrifugal force and it decreases as the distance from nozzle to plate increases. In impingement zone and radial wall jet, the spread of flow increases as the angular velocity decreases The numerical results give good agreement with the experiment data of Minagawa and Obi (Int. J. of Heat and Fluid Flow 2004; 25 :759–766). Copyright © 2006 John Wiley & Sons, Ltd.     

Combined effect of viscous dissipation and thermal radiation on fluid flows over a non-linearly stretched permeable wall

An analysis is presented for the steady non-linear viscous flow of an incompressible viscous fluid over a horizontal surface of variable temperature with a power-law velocity under the influences of suction/blowing, viscous dissipation and thermal radiation. Numerical results are illustrated by means of tables and graphs. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation. The effects of the stretching parameter n, suction/blowing parameter b, Prandtl number σ, Eckert number E_c(E_c ^* )E_{c}(E_{c}^{ *} ) and radiation parameter N _R are discussed. Two cases are studied, namely, (i) Prescribed surface temperature (PST case) and, (ii) Prescribed heat flux at the sheet (PHF case).     

Unsteady compressible boundary layer flow over a circular cone near a plane of symmetry

An analysis has been performed to study the unsteady laminar compressible boundary layer governing the hypersonic flow over a circular cone at an angle of attack near a plane of symmetry with either inflow or outflow in the presence of suction. The flow is assumed to be steady at time t=0 and at t>0 it becomes unsteady due to the time-dependent free stream velocity which varies arbitrarily with time. The nonlinear coupled parabolic partial differential equations under boundary layer approximations have been solved by using an implicit finite-difference method. It is found that suction plays an important role in stabilising the fluid motion and in obtaining unique solution of the problem. The effect of the cross flow parameter is found to be more pronounced on the cross flow surface shear stress than on the streamwise surface shear stress and surface heat transfer. Beyond a certain value of the cross flow parameter overshoot in the cross flow velocity occurs and the magnitude of this overshoot increases with the cross flow parameter. The time variation of the streamwise surface shear stress is more significant than that of the cross flow surface shear stress and surface heat transfer. The suction and the total enthalpy at the wall exert strong influence on the streamwise and cross flow surface shear stresses and the surface heat transfer except that the effect of suction on the cross flow surface shear stress is small.     

Extension of the problem of designing a wing airfoil with active flow controls to the case of systems involving a screen

The solution of the inverse boundary-value problem for a wing airfoil with slot air suction from the outer flow on its upper surface and control jet injection from its rear is generalized to include the case of the flow around such an airfoil in the presence of a screen. The complications due to the double connectivity of the flow region are overcome by means of introducing a fictitious flow beneath the screen. The solution is constructed using a numerical-analytical iteration procedure. Formulas for recalculating the aerodynamic characteristics and the velocity distribution over the airfoil surface to different flight regimes and suction-injection device operation regimes are derived. The effect of the injected jet energy, the airfoil-screen spacing, and the slope of the rectilinear airfoil undersurface on the aerodynamic and geometric characteristics of the airfoil, namely, the shape and the lift coefficient, is studied. The reliability of the results is confirmed by the results of calculations using the Fluent program.     

An exact solution of boundary layer flow over a moving surface embedded into a nanofluid in the presence of magnetic field and suction/injection

The effects of magnetic field, suction/injection, nanoparticles type, and nanoparticle volume fraction on heat transfer characteristics and mechanical properties of a moving surface embedded into cooling medium consists of water with Cu, Ag or Al₂O₃ particles are studied. The governing boundary layer equations are transformed to ordinary differential equations containing, suction/injection parameter, magnetic parameter, nanoparticle and volume fraction. These equations are solved analytically. The velocity and temperature profiles within the boundary layer are plotted and discussed in details for various values of the different parameters.     

Numerical investigation of turbulent free jet flows issuing from rectangular nozzles: the influence of small aspect ratio

In this research, the fluid and thermal characteristics of a rectangular turbulent jet flow is studied numerically. The results of three-dimensional jet issued from a rectangular nozzle are presented. A numerical method employing control volume approach with collocated grid arrangement was employed. Velocity and pressure fields are coupled with SIMPLEC algorithm. The turbulent stresses are approximated using k–e{\varepsilon} model with two different inlet conditions. The velocity and temperature fields are presented and the rates of their decay at the jet centerline are noted. The velocity vectors of the main flow and the secondary flow are illustrated. Also, effect of aspect ratio on mixing in rectangular cross-section jets is considered. The aspect ratios that were considered for this work were 1:1 to 1:4. The results showed that the jet entrains more with smaller AR. Special attention has been drawn to the influence of the Reynolds number (based on hydraulic diameter) as well as the inflow conditions on the evolution of the rectangular jet. An influence on the jet evolution is found for smaller Re, but the jet is close to a converged state for higher Reynolds numbers. The inflow conditions have considerable influence on the jet characteristics.     

Effect of novel synthetic jet on wake vortex shedding modes of a circular cylinder

A novel actuator signal achieved by changing the ratio of the suction duty cycle to the blowing duty cycle is adopted to enhance the control effect of the synthetic jet for the flow around a circular cylinder. The suction duty cycle factor k defined as the ratio between the time duration of the suction cycle and the blowing cycle and the equivalent momentum coefficient C_μ are introduced as the determining parameters. The synthetic jet is positioned at the rear stagnation point in order to introduce symmetric perturbations upon the flow field. The proper orthogonal decomposition (POD) technique is applied for the analysis of the spanwise vorticity field. Increasing the suction duty cycle factor, the momentum coefficient is enhanced, and thus a stronger and larger scale synthetic jet vortex pair with a higher convection velocity is generated. The synthetic jet vortex pair interacts with the spanwise vorticity shear layers behind both sides of the cylinder, resulting in the variations of the wake vortex shedding modes at Re=950: for k=0.25, C_μ=0.148, vortex synchronization at the subharmonic excitation frequency with antisymmetric shedding mode; for 0.50≤k≤1.00, 0.213≤C_μ≤0.378, vortex synchronization at the excitation frequency with the symmetric or antisymmetric shedding modes; for 2.00≤k≤4.00, 0.850≤C_μ≤2.362, vortex synchronization at the excitation frequency with symmetric shedding mode. Hence, the control effect of the synthetic jet upon the wake vortex of a circular cylinder can be enhanced by increasing the suction duty cycle factor so as to increase the momentum coefficient. This is also validated at a higher Reynolds number Re=1600.