Numerical studies of slow viscous rotating flow past a sphere—1

The Navier-Stokes equations for a steady, viscous rotating fluid, rotating about the z-axis with angular velocity ω are linearized using the Stokes approximation. The linearized Navier-Stokes equations governing the axisymmetric flow can be written as three coupled partial differential equations for the stream function, vorticity and rotational velocity components. One parameter, R_eω = 2ωa²/v, enters the resulting equations. For R_eω « 1, the coupled equations are solved by the Peaceman-Rachford A.D.I. (Alternating Direction Implicit) method and the resulting algebraic equations are solved by the ‘method of sweeps’. Stream lines for ψ = 0·05, 0·2, 0·5 and magnitude of the vorticity vector z = 0·2 are plotted for R_eω = 0·1, 0·3, 0·5. Correction to the Stokes drag due to the rotation of fluid is calculated.     

Drag reduction by polymer solutions in a riblet-lined pipe

The flow of 3 to 100 wppm aqueous solutions of a polyethyleneoxide polymer,M _w=6.2×;10⁶, was studied in a 10.2 mm i.d. pipe lined with 0.15 mm V-groove riblets, at diametral Reynolds numbers from 300 to 150000. Measurements in the riblet pipe were accompanied by simultaneous measurements in a smooth pipe of the same diameter placed in tandem. The chosen conditions provided turbulent drag reductions from zero to the asymptotic maximum possible. The onset of polymer-induced drag reduction in the riblet pipe occurred at the same wall shear stress, * _w =0.65 N/m², as that in the smooth pipe. After onset, the polymer solutions in the riblet pipe initially exhibited linear segments on Prandtl-Karman coordinates, akin to those seen in the smooth pipe, with specific slope increment . The maximum drag reduction observed in the riblet pipe was independent of polymer concentration and well below the asymptotic maximum drag reduction observed in the smooth pipe. Polymer solution flows in the riblet pipe exhibited three regimes: (i) Hydraulically smooth, in which riblets induced no drag reduction, amid varying, and considerable, polymer-induced drag reduction; this regime extended to non-dimensional riblet heightsh ⁺<5 in solvent andh ⁺<10 in polymer solutions. (ii) Riblet drag reduction, in which riblet-induced flow enhancementR>0; this regime extended from 5<h ⁺<22 in solvent and from 10<h ⁺<30 in the 3 wppm polymer solution, with respective maximaR=0.6 ath ⁺=14 andR=1.6 ath ⁺=21. Riblet drag reduction decreased with increasing polymer concentration and increasing polymer-induced flow enhancement S. (iii) Riblet drag enhancement, whereinR<0; this regime extended for 22<h ⁺<110 in solvent, withR;–2 forh ⁺>70, and was observed in all polymer solutions at highh ⁺, the more so as polymer-induced drag reduction increased, withR<0 for allS>8. The greatest drag enhancement in polymer solutions,R=–7±1 ath ⁺=55 whereS=20, considerably exceeded that in solvent. Three-dimensional representations of riblet- and polymer-induced drag reductions versus turbulent flow parameters revealed a hitherto unknown dome region, 8<h ⁺<31, 0<S<10, 0<R<1.5, containing a broad maximum at (h ⁺,S,R) = (18, 5, 1.5). The existence of a dome was physically interpreted to suggest that riblets and polymers reduce drag by separate mechanisms.     

Numerical studies of slow viscous rotating flow past a sphere. III

The flow of steady incompressible viscous fluid rotating about the z-axis with angular velocity ω and moving with velocity u past a sphere of radius a which is kept fixed at the origin is investigated by means of a numerical method for small values of the Reynolds number Re_ω. The Navier–Stokes equations governing the axisymmetric flow can be written as three coupled non-linear partial differential equations for the streamfunction, vorticity and rotational velocity component. Central differences are applied to the partial differential equations for solution by the Peaceman–Rachford ADI method, and the resulting algebraic equations are solved by the ‘method of sweeps’. The results obtained by solving the non-linear partial differential equations are compared with the results obtained by linearizing the equations for very small values of Re_ω. Streamlines are plotted for Ψ = 0·05, 0·2, 0·5 for both linear and non-linear cases. The magnitude of the vorticity vector near the body, i.e. at z = 0·2, is plotted for Re_ω = 0·05, 0·24, 0·5. The correction to the Stokes drag as a result of rotation of the fluid is calculated.     

Effect of rounding side-corners on aerodynamic forces and turbulent wake of a cube placed on a ground plane

This paper describes the experimental study of a flow past a cube with rounded side-corners placed in a ground plane under the condition of δ/D < 1, where δ is the thickness of the upstream boundary layer. The experiment was carried out in an N.P.L. type wind-tunnel having a working section of 500 mm×500 mm × 2,000 mm at a Reynolds number 4.74×10⁴. The suface-pressure distribution on the cube was measured, and the drag coefficient was determined from the surface-pressure distribution. Furthermore, two kinds of vortices generated around the cube were observed. The distribution of velocities and turbulent intensities in the turbulent wake behind the cube with rounded side corners were measured, and compared with those of a two-dimensional cylinder. As a result, it was found that the drag coefficient decreases rapidly in the range of 0 ≦ 2R/D ≦ 0.3, and the Strouhal number for the arch-vortex shedding increases as the radius of the corner increases. A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, 17–19 October 1988     

Numerical modelling of confined flow past a cylinder of square cross-section at various orientations

Results are presented for the unsteady, two-dimensional flow and heat transfer due to a square obstruction of diameter d located asymmetrically between the parallel sliding walls of a channel with length-to-height ratio W/H = 6·44. Analysis is based on the numerical solution of spatially and temporally second-order accurate finite difference approximations of the transport equations expressed in curvilinear co-ordinates. Laminar, constant property flow is assumed for obstruction configurations in which the blockage ratio is d/H = 0·192, the nearest-wall distances are g/d = 0·2, 0·5 and 1, the orientation angles are α=0°, 10° and 20° and the Reynolds numbers are Re=100, 500, and 1000. Preparatory testing of the numerical procedure was performed for a variety of documented flows to verify its physiconumerical accuracy and obtain estimates of the residual grid-dependent uncertainties in the variables calculated. Heat transfer, drag and lift coefficients and Strouhal numbers for the present flow were finally calculated to within 4%–7% of their grid-dependent values using non-uniformly spaced grids consisting of (x=99, y=55) nodes. Above a critical value of the Reynolds number, which depends on the geometrical parameters, the flow is characterized by alternate vortex shedding from the obstruction top and bottom surfaces. Streamline, vorticity and particle streakline plots provide qualitative impressions of the unsteady vortical flow. Especially noteworthy are the extremes in the lift coefficient which ranges from large positive values for an obstruction with g/d=0·2 and α=10° to negative values for one with g/d=0·5 and α=0°. Both the drag and lift coefficients as well as the Strouhal number exhibit non-monotonic variations with respect to the parameters explored. Asymmetries in the obstruction location and orientation account for relatively large vortex-induced periodic variations in heat transfer, especially along the wall nearest the obstruction. Notable differences are also predicted for the heat transfer coefficients of the individual obstruction surfaces as a function of the orientation angle.     

Effect of magnetic Reynolds number on the two‐dimensional hydromagnetic flow around a cylinder

Numerical experiments have been conducted to study the effect of magnetic Reynolds number on the steady, two‐dimensional, viscous, incompressible and electrically conducting flow around a circular cylinder. Besides usual Reynolds number Re, the flow is governed by the magnetic Reynolds number R_m and Alfvén number β. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The pressure Poisson equation is solved to find the pressure fields in the entire flow region. The effects of the magnetic field and electrical conductivity on the recirculation bubble, drag coefficient, standing vortex and pressure are presented and discussed. For low interaction parameter (N<1), the suppression of the flow‐separation is nearly independent of the conductivity of the fluid, whereas for large interaction parameters, the conductivity of the fluid strongly influences the control of flow‐separation. Copyright © 2008 John Wiley & Sons, Ltd.     

A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement

This paper describes a numerical study of the two‐dimensional and three‐dimensional unsteady flow over two square cylinders arranged in an in‐line configuration for Reynolds numbers from 40 to 1000 and a gap spacing of 4D, where D is the cross‐sectional dimension of the cylinders. The effect of the cylinder spacing, in the range G = 0.3D to 12D, was also studied for selected Reynolds numbers, that is, Re = 130, 150 and 500. An incompressible finite volume code with a collocated grid arrangement was employed to carry out the flow simulations. Instantaneous and time‐averaged and spanwise‐averaged vorticity, pressure, and streamlines are computed and compared for different Reynolds numbers and gap spacings. The time averaged global quantities such as the Strouhal number, the mean and the RMS values of the drag force, the base suction pressure, the lift force and the pressure coefficient are also calculated and compared with the results of a single cylinder. Three major regimes are distinguished according to the normalized gap spacing between cylinders, that is, the single slender‐body regime (G < 0.5), the reattach regime (G < 4) and co‐shedding or binary vortex regime (G ≥4). Hysteresis with different vortex patterns is observed in a certain range of the gap spacings and also for the onset of the vortex shedding. Copyright © 2011 John Wiley & Sons, Ltd.     

Effects of a trapped vortex cell on a thick wing airfoil

The effects of a trapped vortex cell (TVC) on the aerodynamic performance of a NACA0024 wing model were investigated experimentally at Re = 10⁶ and 6.67×10⁵6.67\times 10^{5}. The static pressure distributions around the model and the wake velocity profiles were measured to obtain lift and drag coefficients, for both the clean airfoil and the controlled configurations. Suction was applied in the cavity region to stabilize the trapped vortex. For comparison, a classical boundary layer suction configuration was also tested. The drag coefficient curve of the TVC-controlled airfoil showed sharp discontinuities and bifurcative behavior, generating two drag modes. A strong influence of the angle of attack, the suction rate and the Reynolds number on the drag coefficient was observed. With respect to the clean airfoil, the control led to a drag reduction only if the suction was high enough. Compared to the classical boundary layer suction configuration, the drag reduction was higher for the same amount of suction only in a specific range of incidence, i.e., α = −2° to α = 6° and only for the higher Reynolds number. For all the other conditions, the classical boundary layer suction configuration gave better drag performances. Moderate increments of lift were observed for the TVC-controlled airfoil at low incidence, while a 20% lift enhancement was observed in the stall region with respect to the baseline. However, the same lift increments were also observed for the classical boundary layer suction configuration. Pressure fluctuation measurements in the cavity region suggested a very complex interaction of several flow features. The two drag modes were characterized by typical unsteady phenomena observed in rectangular cavity flows, namely the shear layer mode and the wake mode.     

Equilibrium states in homogeneous turbulence with baroclinic instability

The evolution of energies and fluxes in homogeneous turbulence with baroclinic instability is analyzed using the linear theory. The mean flow corresponds to a vertical shear having a uniform mean velocity gradient, ?U _i /?x _j  = S δ _i1 δ _j3, a system rotation about the vertical axis with rate Ω, Ω _i  = Ωδ _i3, and uniform buoyancy gradients in the spanwise ${(\partial B{/}\partial x_2\,{=}\, N_h^2\,{=}\,-2\Omega S)}The evolution of energies and fluxes in homogeneous turbulence with baroclinic instability is analyzed using the linear theory. The mean flow corresponds to a vertical shear having a uniform mean velocity gradient, ∂U _i /∂x _j  = S δ _i1 δ _j3, a system rotation about the vertical axis with rate Ω, Ω _i  = Ωδ _i3, and uniform buoyancy gradients in the spanwise (?B/?x₂ = N_h² = -2WS){(\partial B{/}\partial x_2\,{=}\, N_h^2\,{=}\,-2\Omega S)} and vertical (?B/?x₃ = N_v²){(\partial B{/}\partial x_3\,{=}\,N_v^2)} directions. Computations based on the rapid distortion theory (RDT) are performed for several values of the rotation number R = 2Ω/S and the Richardson number R_i = N_v²/S² < 1{R_i\,{=}\,N_v^2/S^2 <1 }. It is shown that, during an initial phase, the energies and the buoyancy fluxes are sensitive to the effects of pressure and viscosity. At large time, the ratios of energies, as well as the normalized fluxes, evolve to an asymptotically constant value, while the pressure–strain correlation scaled with the product of the turbulent kinetic energy by the shear rate approaches zero. Accordingly, an analytical parametric study based on the “pressure-less” approach (PLA) is also presented. The analytical study indicates that, when R _i  < 1, there is an exponential instability and equilibrium states of turbulence, in agreement with RDT. The energies and the buoyancy fluxes grow exponentially for large times with the same rate (γ in St units). The asymptotic value of the ratios of energies yielded by RDT is well described by its PLA counterpart derived analytically. At R _i  = 0, the asymptotic value of γ increases with increasing R approaching 2 for high rotation rates. At low rotation rates, an important contribution to the kinetic energy comes from the streamwise kinetic energy, whereas, at high rotation rates, the contribution of the vertical kinetic energy is dominant. When 0 < R _i  < 1 and R 1 0{R\ne 0}, the asymptotic value of γ decreases as R _i increases so as it becomes zero at R _i  = 1.     

Experimental study of single bubble motion in a liquid metal column exposed to a DC magnetic field

The motion of single Argon bubbles rising in the eutectic alloy GaInSn under the influence of a DC longitudinal magnetic field (parallel to the direction of bubble motion) was examined. The magnetic field strength was varied up to 0.3 T corresponding to a magnetic interaction parameter N (which measures the ratio of electromagnetic forces to inertial forces) slightly greater than 1. The liquid metal was at rest in a cylindrical container. Bubble and liquid velocities were measured using ultrasound Doppler velocimetry (UDV). The measured bubble terminal velocity showed oscillations indicating a zigzag movement of ellipsoidal bubbles. For small bubbles (d_e ⩽ 4.6 mm) an increase of the drag coefficient with increasing magnetic interaction parameter N was observed, whereas for larger bubbles (d_e ⩾ 5.4 mm) the application of the magnetic field reduces the drag coefficient. The measurements revealed a distinct electromagnetic damping of the bubble induced liquid velocity leading to more rectilinear bubble trajectories when the magnetic field is applied. Moreover, significant modifications of the bubble wake structure were observed. Raising of the magnetic field strength caused an enlargement of the eddies in the wake. The Strouhal number decreases with increasing magnetic interaction parameter N.     

Two-dimensional unsteady laminar flow of a power law fluid across a square cylinder

The two-dimensional and unsteady free stream flow of power law fluids past a long square cylinder has been investigated numerically in the range of conditions 60≤Re≤160 and 0.5≤n≤2.0. Over this range of Reynolds numbers, the flow is periodic in time. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The global quantities such as drag coefficients, Strouhal number and the detailed kinematic variables like stream function, vorticity and so on, have been obtained for the above range of conditions. While, over this range of Reynolds number, the flow is known to be periodic in time for Newtonian fluids, a pseudo-periodic flow regime displaying more than one dominant frequency in the lift is observed for shear-thinning fluids. This seems to occur at Reynolds numbers of 120 and 140 for n=0.5 and 0.6, respectively. Broadly speaking, the smaller the value of the power law index, lower is the Reynolds number of the onset of the pseudo-periodic regime. This work is concerned only with the fully periodic regime and, therefore, the range of Reynolds numbers studied varies with the value of the power law index. Not withstanding this aspect, in particular here, the effects of Reynolds number and of the power law index have been elucidated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening fluid behaviour delays this separation and shows the lowering of the drag coefficient with the Reynolds number. Also, the preliminary results suggest the transition from the steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thinning fluids than that in Newtonian fluids.     

A numerical study of pulsatile laminar flows in a pipe with a ring-type constriction

Numerical simulations have been carried out to study pulsatile laminar flows in a pipe with an axisymmetric ringtype constriction. Three types of pulsatile flows were investigated, namely a physiological flow, a pure sinusoidal flow and a non-zero mean velocity sinusoidal flow. The laminar flow governing equations were solved by the SIMPLE algorithm on a non-staggered grid and a modified Crank-Nicolson approximation was used to discretrize the momentum equations with respect to time. The maximum flow Reynolds numer (Re) is 100. The Womersley number (N_w) ranges from 0 to 50, with the corresponding Strouhal number (St) ranging from 0 to 3·98. The constriction opening ratio (d/D) and thickness ratio (h/D) are fixed at 0·5 and 0·1 respectively. Within the time period investigated, all these pulsatile flows include both forward and backward flows. The unsteady recirculation region and the recirculation points change in size and location with time. For N_w ≤ 1 and St≤ 1·56 x 10^?3 the three pulsatile flows have the same simple relation between the instantaneous flow rate and pressure loss (Δp) across the constriction and the pressure gradient in the axial direction (dp/dz) in the fully developed flow region. The phase angles between the flow rate and pressure loss and the pressure gradient are equal to zero. With increasing N_w and St, the phase angle between the flow rate and the dp/dz becomes larger and has its maximum value of 90° at N_w = 50 and St = 3·98. The three pulsatile flows also show different relations between the flow rate and the pressure gradient. The pure sinusoidal flow has the largest maximum pressure gradient and the non-zero mean velocity sinusoidal flow has the smallest. For larger N_w and St the fully developed velocity profiles in the fully developed flow region have a smaller velocity gradient along the radial direction in the central region. The maximum recirculation length increases for N_w ranging from 0 to 4·2, while this length becomes very small at N_w = 50 and St = 3·98. The deceleration tends to enlarge the recirculation region and this effect appears for N_w ≥ 3 and St ≥ 1·43×10^?2. Linear relations exist between the flow rate and the instantaneous maximum values of velocity, vorticity and shear stress.     

Prediction of flow and heat transfer in narrow rotating rectangular channels using Reynolds stress model

A computational study is performed on three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with aspect ratio (AR) of 10:1, oriented 120° from the direction of rotation. The Focus is on high rotation and high-density ratios effects on the heat transfer characteristics of the 120° orientation. The Reynolds stress model (RSM), which accounts for rotational effects are used to compute the turbulent flow and heat transfer in the rotating channel. The effects of rotation and coolant-to-wall density ratio on the fluid flow and heat transfer characteristics is reported on a range of rotation numbers and density ratios (0 < Ro < 0.25 and 0.07 < Δρ/ρ < 0.4). The computational results are in good agreement with experimental data within ±15%. The results show that the density ratio, rotation number and channel orientation significantly affect the flow field and heat transfer characteristics in the rotating rectangular channel. Flow reversal occurs at high rotation number and density ratio.     

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.     

Flow structure of wake behind a rotationally oscillating circular cylinder

Flow around a circular cylinder oscillating rotationally with a relatively high forcing frequency has been investigated experimentally. The dominant parameters affecting this experiment are the Reynolds number (Re), oscillation amplitude (θ_A), and frequency ratio F_R=f_f/f_n, where f_f is the forcing frequency and f_n is the natural frequency of vortex shedding. Experiments were carried out under conditions of Re=4.14×10³, 0°θ_A60° and 0.0F_R2.0. Rotational oscillation of the cylinder significantly modified the flow structure in the near-wake. Depending on the frequency ratio F_R, the cylinder wake showed five different flow regimes, each with a distinct wake structure. The vortex formation length and the vortex shedding frequency were greatly changed before and after the lock-on regime where vortices shed at the same frequency as the forcing frequency. The lock-on phenomenon always occurred at F_R=1.0 and the frequency range of the lock-on regime expanded with increasing oscillation amplitude θ_A. In addition, the drag coefficient was reduced when the frequency ratio F_R was less than 1.0 (F_R<1.0) while fixing the oscillation amplitude at θ_A=30°. When the oscillation amplitude θ_A was used as a control parameter at a fixed frequency ratio F_R=1.0 (lock-on regime), the drag reduction effect was observed at all oscillation amplitudes except for the case of θ_A=30°. This type of active flow control method can be used effectively in aerodynamic applications while optimizing the forcing parameters.     

Aerodynamic Performance of a Gliding Swallowtail Butterfly Wing Model

In the present study, we perform a wind-tunnel experiment to investigate the aerodynamic performance of a gliding swallowtail-butterfly wing model having a low aspect ratio. The drag, lift and pitching moment are directly measured using a 6-axis force/torque sensor. The lift coefficient increases rapidly at attack angles less than 10° and then slowly at larger attack angles. The lift coefficient does not fall off rapidly even at quite high angles of attack, showing the characteristics of low-aspect-ratio wings. On the other hand, the drag coefficient increases more rapidly at higher angles of attack due to the increase in the effective area responsible for the drag. The maximum lift-to-drag ratio of the present modeled swallowtail butterfly wing is larger than those of wings of fruitfly and bumblebee, and even comparable to those of wings of birds such as the petrel and starling. From the measurement of pitching moment, we show that the modeled swallowtail butterfly wing has a longitudinal static stability. Flow visualization shows that the flow separated from the leading edge reattaches on the wing surface at α < 15°, forming a small separation bubble, and full separation occurs at α ≥ 15°. On the other hand, strong wing-tip vortices are observed in the wake at α ≥ 5° and they are an important source of the lift as well as the main reason for broad stall. Finally, in the absence of long hind-wing tails, the lift and longitudinal static stability are reduced, indicating that the hind-wing tails play an important role in enhancing the aerodynamic performance.     

Critical blowup and global existence numbers for a weakly coupled system of reaction-diffusion equations

Let D ⊂ R ^N be either all of R ⁿ or else a cone in R ^N whose vertex we may take to be at the origin, without loss of generality. Let p _i, q_j, i = 1, 2, be nonnegative with 0<p ₁+q ₁≦p ₂+q ₂. We consider the long-time behavior of nonnegative solutions of the system

Drag Reduction of a Circular Cylinder Using an Upstream Rod

Experimental studies on the drag reduction of the circular cylinder were conducted by pressure measurement at a Reynolds number of 82 000 (based on the cylinder diameter). A rod was placed upstream of and parallel to the cylinder to control the flow around the cylinder. The upstream rod can reduce the resultant force of the cylinder at various spacing between the rod and the cylinder for α < 5^∘(α defined as the staggered angle of the rod and the cylinder). For α > 10^∘, the resultant force coefficient has a large value, so the upstream rod cannot reduce the force on the cylinder any more. For α = 0^∘ and d/D = 0.5 (where d and D are the diameter of the rod and the cylinder, respectively), the maximum drag of the cylinder reduces to 2.34% that of the single cylinder. The mechanism of the drag reduction of the cylinder with an upstream rod in tandem was presented by estimating the local contributions to the drag reduction of the pressure variation. In the staggered arrangement, the flow structures have five flow patterns (they are the cavity mode, the wake splitting mode, the wake merge mode, the weak boundary layer interaction mode and the negligible interaction mode) according to the pressure distribution and the hydrogen bubble flow visualization. The half plane upwind of the cylinder can be divided to four regions, from which one can easily estimates the force acting on the circular cylinder with an upstream rod in staggered arrangement.     

NUMERICAL STUDY OF EFFECTS OF PULSATILE AMPLITUDE ON UNSTEADY LAMINAR FLOWS IN RIGID PIPE WITH RING-TYPE CONSTRICTIONS

The effects of pulsatile amplitude on sinusoidal laminar flows through a rigid pipe with sharp-edged ring-type constrictions have been studied numerically. The parameters considered are: mean Reynolds number (Re) of the order of 100; Strouhal number (St) in the range 0·0–3·98; Womersley number (Nw) in the range 0·0–50·0. The pulsatile amplitude (A) varies in the range 0·0–2·0. The flow characteristics were studied through the pulsatile contours of streamline, vorticity, shear stress and isobars. Within a pulsatile cycle the relations between instantaneous flow rate (Q) and instantaneous pressure gradient (dp/dz) are observed to be elliptic. The relations between instantaneous flow rate (Q) and pressure loss (P_loss) are quadratic. Linear relations exist between instantaneous flow rate (Q) and maximum velocity, maximum vorticity and maximum shear stress. © by 1997 John Wiley & Sons, Ltd.     

Effect of distributed gas injection on aerodynamic characteristics of a body of revolution in a supersonic flow

Results of experimental and numerical investigations of the effect of gas injection through a permeable porous surface on the drag coefficient of a cone-cylinder body of revolution in a supersonic flow with the Mach number range M _h = 3–6 are presented. It is demonstrated that gas injection through a porous nose cone with gas flow rates being 6–8% of the free-stream flow rate in the mid-section leads to a decrease in the drag coefficient approximately by 5–7%. The contributions of the decrease in the drag force acting on the model forebody and of the increase in the base pressure to the total drag reduction are approximately identical. Gas injection through a porous base surface with the flow rate approximately equal to 1% leads to a threefold increase in the base pressure and to a decrease in the drag coefficient. Gas injection through a porous base surface with the flow rate approximately equal to 5% gives rise to a supersonic flow zone in the base region.