Showing papers on "Freestream published in 2009"

Turbulence Model Behavior in Low Reynolds Number Regions of Aerodynamic Flowfields

Abstract: The behaviors of the widely used Spalart-Allmaras and Menter shear-stress transport turbulence models at low Reynolds numbers and under conditions conducive to relaminarization are documented. The flows used in the investigation include 2-D zero-pressure-gradient flow over a flat plate from subsonic to hypersonic Mach numbers, 2-D airfoil flow from subsonic to supersonic Mach numbers, 2-D subsonic sink flow, and 3-D subsonic flow over an infinite swept wing (particularly its leading-edge region). Both models exhibit a range over which they behave "transitionally" even with inflow values set to cause immediate growth of the turbulence quantities, in the sense that the flow is neither laminar nor fully turbulent, but these behaviors are different: the shear-stress transport model typically has a well-defined transition location, whereas the Spalart-Allmaras model does not. Both models are predisposed to delayed activation of turbulence with increasing freestream Mach number. Also, both models can be made to achieve earlier activation of turbulence by increasing their freestream levels, but too high a level can disturb the turbulent solution behavior. The technique of maintaining freestream levels of turbulence without decay in the shear-stress transport model, introduced elsewhere, is shown here to be useful in reducing grid dependence of the model's transitional behavior. Both models are demonstrated to be incapable of predicting relaminarization; eddy viscosities remain weakly turbulent in accelerating or laterally strained boundary layers for which experiment and direct simulations indicate turbulence suppression. The main conclusion is that these models are intended for fully turbulent high Reynolds number computations, and using them for transitional (e.g., low Reynolds number) or relaminarizing flows is not appropriate. Competing models which fare better in these areas have not been identified.

Receptivity of a Supersonic Boundary Layer to Acoustic Disturbances

Abstract: The boundary layer receptivity process generated by the interaction of 3-D slow and fast acoustic disturbances with a blunted flat plate, is numerically investigated at a freestream Mach number of 3.5, and at a high Reynolds number of 39 * 10 6 /m. The computations are performed with and without a 2-D isolated roughness element located near the leading edge. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the fifth-order accurate weighted essentially nonoscillatory scheme for space discretization and using the third-order total-variation-diminishing Runge-Kutta scheme for time integration. The simulations showed that the linear instability waves are generated very close to the leading edge. The wavelength of the disturbances inside the boundary layer first increases gradually and becomes longer than the wavelength for the instability waves within a short distance from the leading edge. The wavelength then decreases gradually and merges with the wavelength for the Tollmien-Schlichting wave. The initial amplitudes of the instability waves near the neutral points, the receptivity coefficients, are about 1.20 and 0.07 times the amplitude of the freestream disturbances for the slow and fast waves, respectively. It was also revealed that a small isolated roughness element does not enhance the receptivity process for the given nose bluntness.

Stability of Supersonic Boundary Layers on a Cone at an Angle of Attack

Abstract: The stability and receptivity of a three-dimensional hypersonic boundary layer over a 7deg half-angle straight cone at an angle of attack of 6deg is numerically investigated at a freestream Mach number of 6.0 and a Reynolds number of 10.4x10(exp 6)/m. The generation and evolution of stationary crossflow vortices are also investigated by performing simulations with three-dimensional roughness elements located on the surface of the cone. The flow fields with and without the roughness elements are obtained by solving the full Navier- Stokes equations in cylindrical coordinates using a fifth-order accurate weighted essentially non-oscillatory (WENO) scheme for spatial discretization and a third-order total-variation-diminishing (TVD) Runge-Kutta scheme for temporal integration. Stability computations produced azimuthal wavenumbers in the range of m approx. 20-50 for the most amplified traveling disturbances and in the range of m approx.30-70 for the stationary disturbances. The frequency of the unstable second-mode ranges from 400 kHz to 900 kHz along the windward ray. The N-Factor computations predicted transition would occur more forward on the sides of the cone as compared to the transition fronts near the windward and the leeward rays. The simulations also show the crossflow vortices originating from the nose region propagate towards the leeward ray. No perturbations were observed toward the windward half of the cone.

Density field of supersonic separated flow past an afterbody nozzle using tomographic reconstruction of BOS data

Abstract: The background oriented Schlieren (BOS) technique has been applied to determine the density field in an oblique shock-separated turbulent boundary flow. Measurements were made for two cases, namely, with/without jet flow from the afterbody which is a nozzle. In addition, oil flow and Schlieren visualizations were carried out—the results show certain upstream features of interest including shock excursions. The mean density field from BOS is discussed along with results from conventional Schlieren flow visualization. The data extracted from the mean density field obtained through BOS have been compared for the jet-off and jet-on cases. The data obtained also show the mean density in the base region (jet-off case) to be about 50% of the freestream density and match the isentropic values for the underexpanded jet at the exit. The study involving shock–boundary interaction, movement of freestream shock over the afterbody in the presence of a jet plume provides understanding of flow physics in a flow regime where whole field velocity measurements are extremely difficult.

Simulation of Turbulent Mixing Behind a Strut Injector in Supersonic Flow

Abstract: The flowfield downstream of a strut-based injection system in a supersonic combustion ramjet is investigated using large-eddy simulation with a new localized dynamic subgrid closure for compressible turbulent mixing. Recirculations are formed at the base of the strut in the nonreacting flow and trap some of the injected fluid. The high levels of turbulence along the underexpanded hydrogen jets and in the shear layer lead to a high level of mixing of fuel and freestream fluids. Furthermore, the shear layer unsteadiness permits efficient large-scale mixing of freestream and injected fluids. In the reacting flowfield, the flame anchoring mechanism is, however, found to depend more on a recirculation region located downstream of the injectors than on their sides. A region of reverse flow is formed that traps hot products and radicals. Intermittent convection of hot fluid toward the injector occurs and preheats the reactants.

Transition delay in hypervelocity boundary layers by means of CO 2 /acoustic instability interactions

Abstract: A novel method to delay transition in hypervelocity flows over slender bodies by injecting CO2 into the boundary layer of interest is investigated. The results presented here consist of both experimental and computational data. The experimental data was obtained at Caltech’s T5 reflected shock tunnel, while the computational data was obtained at the University of Minnesota. The experimental model was a 5 degree sharp cone, chosen because of its relevance to axisymmetric hypersonic vehicle designs and the wealth of experimental and numerical data available for this geometry. The model was instrumented with thermocouples, providing heat transfer measurements from which transition locations were determined and the efficacy of adding CO2 in delaying transition was gauged. For CO2/N2 freestream blends without injection, the transition Reynolds number more than doubled for mixtures with 40% CO2 mole fraction compared to the case of 100% N2. For the cases with injection, shadowgraph visualizations were obtained, allowing verification of the injection timing. The computations provide encouraging results that for the injection schemes proposed CO2 is reaching high enough temperatures to excite vibrational modes and thus delay transition.

Performance Characteristics of an Annular Conical Aerospike Nozzle with Freestream Effect

Abstract: An experimental investigation has been carried out to study the performance and base pressure characteristics of a Mach 2.0 annular conical aerospike nozzle with and without freestream flow. The effect of cowl length, plug length, and plug contour variation on the nozzle performance and base pressure characteristics is studied. It is observed that the overexpansion shock from the internal nozzle, overexpansion shock on the spike surface, and the expansion fan from the cowl lip of the internal nozzle dominate the overall flowfield development. The presence of freestream flow reduces the nozzle performance by approximately 4% relative to static conditions. Base pressure characteristics are observed to be strongly influenced by the movement of these shocks on the plug surface, and their subsequent interaction with the inner shear layer controls the base-wake closure. Relative to the conical plug conflguration, the contoured plug shows considerably enhanced base pressure characteristics. Real-time pressure measurements on the spike reveal highly unsteady flow in the intermittent region of separation.

Spatially Distributed Forcing and Jet Vectoring with a Plasma Actuator

Abstract: volume momentum balance was used. By shaping the buried electrode along the span of the actuator, the local volume of plasma generated can be controlled, which is related to the local body force. Pressure measurements were takenintheboundarylayerbehindtheactuatortocalculatethemomentumimpartedtothe flowatvariousspanwise locations corresponding to different electrode widths. Particle image velocimetry data were then used to show that spatially varying, steady jets could be created with the use of only one actuator by varying the width of the buried electrode in a quiescent flow. The angle of the jet created, relative to the dielectric, by a plasma synthetic jet is also investigated. By pointing two plasma actuators at each other, an inverted impinging jet can be created as a result of the two independent jets colliding. By altering the strength of one of the jets relative to the other, the angle of separation can be changed. Particle image velocimetry data were taken to show the effects of altering the voltage (strength)appliedtooneoftheactuatorsrelativetotheother.Itwasfoundthat,withthismethod,jetvectoringcould beachieved.Theangleofthejetcouldbecontrolledafull180degthroughsmallchangesinthevoltageappliedtothe electrodes, also in a quiescent flow. Nomenclature D = diameter FB = body force FS = shear force P = power qd;off = dynamic pressure downstream of the actuator (0.035 m) with the plasma off qd;on = dynamic pressure downstream of the actuator (0.035 m) with the plasma on Re = Reynolds number St = Strouhal number U = freestream velocity ud;off = velocity downstream of the actuator (0.035 m) with the plasma off ud;on = velocity downstream of the actuator (0.035 m) with the plasma on W = waviness amplitude � = angle of jet measured counterclockwise � V = voltage differential between exposed electrodes relative to ground � = wavelength

Effects of Large Scale High Freestream Turbulence and Exit Reynolds Number on Turbine Vane Heat Transfer in a Transonic Cascade

Abstract: This paper experimentally and numerically investigates the effects of large scale high freestream turbulence intensity and exit Reynolds number on the surface heat transfer distribution of a turbine vane in a 2D linear cascade at realistic engine Mach numbers. A passive turbulence grid was used to generate a freestream turbulence level of 16% and integral length scale normalized by the vane pitch of 0.23 at the cascade inlet. The base line turbulence level and integral length scale normalized by the vane pitch at the cascade inlet were measured to be 2% and 0.05, respectively. Surface heat transfer measurements were made at the midspan of the vane using thin film gauges. Experiments were performed at exit Mach numbers of 0.55, 0.75, and 1.01, which represent flow conditions below, near, and above nominal conditions. The exit Mach numbers tested correspond to exit Reynolds numbers of 910 5 , 1.0510 6 , and 1.510 6 based on a vane chord. The experimental results showed that the large scale high freestream turbulence augmented the heat transfer on both the pressure and suction sides of the vane as compared to the low freestream turbulence case and promoted a slightly earlier boundary layer transition on the suction surface for exit Mach 0.55 and 0.75. At nominal conditions, exit Mach 0.75, average heat transfer augmentations of 52% and 25% were observed on the pressure and suction sides of the vane, respectively. An increased Reynolds number was found to induce an earlier boundary layer transition on the vane suction surface and to increase heat transfer levels on the suction and pressure surfaces. On the suction side, the boundary layer transition length was also found to be affected by increase changes in Reynolds number. The experimental results also compared well with analytical correlations and computational fluid dynamics predictions. DOI: 10.1115/1.2952381

Numerical study of plasma-assisted aerodynamic control for hypersonic vehicles

Abstract: different volumetric energy deposition patterns are considered: a spherical pattern, a “pancake” pattern (oblate spheroid), and a “bean” pattern (prolate spheroid). The effectiveness of volumetric energy deposition for flight control appears to scale strongly with a nondimensional parameter based on the freestream flow kinetic energy flux.

Low-Reynolds Number Wing Response to an Oscillating Freestream with and without Feed Forward Control

Abstract: The unsteady lift of a low Reynolds number wing in an oscillating freestream is documented in terms of its amplitude and phase. The phase variation of the lift relative to the freestream velocity shows a larger phase difference than predicted by classical unsteady flow theory. A constant time delay between the lift and the actuator was observed to be τ + =tdelayU/c = 5.3 when normalized by the freestream speed and chord. Feed forward control of pulsed-jet actuators is used to modulate the lift coefficient of the wing, in an attempt to suppress the lift oscillations. Suppression of the fluctuating lift at the fundamental frequency was partially successful, but additional “noise” was added to harmonics of the lift signal by the controller.

Bluntness Impact on Lift-to-Drag Ratio of Hypersonic Wedge Flow

Abstract: simulation Monte Carlo method. The results highlight the sensitivity of the heat transfer coefficient, the total drag coefficient, the total lift coefficient, and the lift-to-drag ratioto changesnot only onthe angle of attack but alsoon the frontal-face thickness of the leading edges. Some significant differences between sharp and blunt leading edges were noted on the surface quantities. Interesting features observed in these surface properties showed that even small leading-edge thickness, compared with the freestream mean free path, still has important effects on high Mach number leading-edge flows. The analysis is important because it is impossible to achieve ideally sharp leading edges of airframes such as waveriders.

Hypersonic turbulent flow simulation of FIRE II reentry vehicle afterbody

Abstract: Thispaperpresentsanumericalinvestigation ofthehypersonicreacting flowaroundtheFIREIIreentrycapsule. At the chosen freestream conditions, the forebody boundary layer and the separated flow on the afterbody are turbulent. The Reynolds-averaged Navier–Stokes method along with two commonly used turbulence models are usedtocomputethe flowfield.Accuratepredictionofturbulentseparated flowathypersonicconditionsischallenging due to the limitations of the underlying turbulence models. The presence of turbulent eddy viscosity in the flow simulation results in a smaller separation bubble than the laminar solution at identical conditions. Also, the two turbulence models predict different levels of eddy viscosity in the neck region. This has a dominant effect on the separation bubble size and the surface pressure. On the other hand, the eddy viscosity values in the near-wall region determine the heat transfer rate to the body. The two models predict comparable heating rates on the conical frustum, and the results match in-flight measurement well. By comparison, surface pressure predictions are appreciably higher than the data.

Suppression of the unsteady vortex wakes of a circular cylinder pair by a doublet-like counter-rotation

Abstract: The present investigation examines the suppression of unsteady, two-dimensional wake instabilities of a pair of identical circular cylinders, placed side-by-side normal to freestream at a low Reynolds number of 150. It is found that when the cylinders are counter-rotated, unsteady vortex wakes can be completely suppressed. At fast enough rotational speeds, a virtual elliptic body is produced by a closed streamline, strongly resembling a doublet potential flow. Copyright © 2009 John Wiley & Sons, Ltd.

Direct Numerical Simulation of a eflected-Shock- Wave/Turbulent-Boundary-Layer Interaction

Abstract: A direct numerical simulation of a reflected-shock-wave/turbulent-boundary-layer interaction at Mach 2.9 and Re θ = 2300 with a flow deflection through the incident shock of 12 deg is presented. A modified weighted essentially nonoscillatory method is used for the spatial discretization of the inviscid fluxes. The numerical scheme has previously been validated in the direct numerical simulation of a compression-ramp interaction against experiments at matching conditions. The flowfield for the present simulation is visualized using a numerical schlieren technique, and a movie of the flow reveals the unsteady shock motion. From the wall-pressure signal in the interaction region and pressure measurements in the freestream, the characteristic low frequency of the shock motion is inferred and found to agree with a scaling previously proposed. The evolution of the mean and fluctuating flow quantities through the interaction is studied. It is observed that the turbulence levels are greatly amplified in the downstream flow and that significant departures from the strong Reynolds analogy occur.

Aerodynamic Characteristics of Asymmetric Bluff Bodies

Abstract: The wake of asymmetric bluff bodies was experimentally measured using particle imaging velocimetry, laser Doppler anemometry, load cell, hotwire, and flow visualization techniques at Re=2600–8500 based on the freestream velocity and the characteristic height of the bluff bodies. Asymmetry is produced by rounding some corners of a square cylinder and leaving others unrounded. It is found that, with increasing corner radius, the flow reversal region is expanded, and the vortex formation length is prolonged. Accordingly, the vortex shedding frequency increases and the base pressure rises, resulting in a reduction in the mean drag as well as the fluctuating drag and lift. It is further found that, while the asymmetric cross section of the cylinder causes the wake centerline to shift toward the sharp corner side of the bluff body, the wake remains globally symmetric about the shifted centerline. The near wake of asymmetric bluff bodies is characterized in detail, including the Reynolds stresses, characteristic velocity, and length scale, and is further compared with that of the symmetric ones.

In situ calibration of hot wire probes in turbulent flows

Abstract: A method for in situ calibration of hot-wires in a turbulent flow is presented. The method is particularly convenient (even necessary) for calibrating large probe arrays, like the 143-wire boundary layer rake of the WALLTURB experiment. It is based on polynomial expansion of the velocity statistics in terms of voltage statistics as originally described by George et al. [Exp Ther Fluid Sci 2(2):230–235, 1989]. Application of the method requires knowing reference mean velocity and higher order central moments (with the array in place) of the turbulent velocity at the probe location at only one freestream velocity. These were obtained in our experiment by a stereo PIV plane just upstream of the probe array. Both the procedure for implementing the method and sample results are presented in the article.

Particle image velocimetry study of flow near trashrack models.

Abstract: This paper provides results of an experimental study of turbulent flow near trashrack models that are comprised of an array of three rectangular bars. The bar thickness, bar depth, and center-to-center spacing were maintained constant. The flow characteristics were studied by aligning the bars with the approach flow and conducting measurements at three different approach freestream velocities. Subsequently, the freestream velocity was kept constant and detailed measurements were conducted for four different bar inclinations relative to the approach flow. For each test condition, a high-resolution particle image velocimetry (PIV) technique was used to conduct detailed velocity measurements in streamwise-spanwise planes at middepth of flow. From these measurements, isocontours and profiles of the mean velocities, turbulence intensities, Reynolds shear stress, and production term in the transport equation for the turbulent kinetic energy were obtained to study the flow characteristics around and downstream of the aligned and inclined bars. Flow characteristics near hydroelectric station trashracks are important for efficient turbine operation and reduction of fish entrainment.

Aero-Acoustic Coupling Inside Large Deep Cavities at Low-Subsonic Speeds

Abstract: Aero-acoustic coupling inside a deep cavity is present in many industrial processes. This investigation focuses on the pressure amplitude response, within two deep cavities characterized by their length over depth ratios (L/H=0.2 and 0.41), as a function of freestream velocities of a 2 X2 m 2 wind tunnel. Convection velocity of instabilities was measured along the shear layer, using velocity cross-correlations. Experiments have shown that in deep cavity for low Mach numbers, oscillations of discrete frequencies can be produced. These oscillations appear when the freestream velocity becomes higher than a minimum value. Oscillations start at L/ θ 0 =10 and 21 for L/H = 0.2 and 0.41, respectively. The highest sound pressure level inside a deep cavity is localized at the cavity floor. A quite different behavior of the convection velocity was observed between oscillating and nonoscillating shear-layer modes. The hydrodynamic mode of the cavity shear layer is well predicted by the Rossiter model (1964, "Wind Tunnel Experiments on the Flow Over Rectangular Cavities at Subsonic and Transonic Speeds," Aeronautical Research Council Reports and Memo No. 3438) when measured convection velocity is used and the empirical time delay is neglected. For LIH =0.2, only the first Rossiter mode is present. For L/H =0.41, both the first and the second modes are detected with the second mode being the strongest.

Plasma flow control - autonomous lift improvement by slope-seeking

Abstract: The present paper constitutes the first experimental attempt of closed-loop separation control using plasma actuators using a slope-seeking algorithm. The post-stall separated flow over a NACA 0015 airfoil is controlled using a single dielectric barrier discharge actuator at the leading edge. Open-loop measurements are first performed to highlight the effects of the voltage amplitude on the control authority for freestream velocities of 10 to 30 m/s (Re=1.3 x 10 to 4 x 10). The results indicate that partial or full reattachment can be achieved and motivate the choice of the slope-seeking algorithm. Then a single-input/ single-output algorithm is used to autonomously seek the optimal voltage required to achieve the control objective (full flow reattachment associated with maximum lift). The paper briefly introduces the concept of slope-seeking, and a detailed parameterization of the controller is considered. Static (fixed speed) closed-loop experiments are then discussed, which demonstrate the capability of the algorithm. In each case, the flow can be reattached in an autonomous fashion. The last part of the paper demonstrates the robustness of the gradient-based, model-free scheme for dynamic freestream conditions. The air flow, initially at 10 m/s, is increased in steps of 10 m/s up to 30 m/s, while the autonomous control scheme attempts to maintain fully attached flow. The results indicate that the control objective can again be achieved in this dynamic experiment.

Critical Design Parameters for Pylon-Aided Gaseous Fuel Injection

Abstract: The Air Force Institute of Technology and the Air Force Research Lab are investigating means to increase the efficiency of fuel-air mixing into supersonic flow upstream of a flame holding cavity. Previous work has shown much promise in increasing the penetration and mixing of a fuel-air mixture into the freestream by injecting fuel behind small triangular pylons. In this paper five triangular pylons of varying widths were examined within a CFD environment. Pylons with a width less than 2-diameters featured a fuel plume flow structure dominated by two sets of counter-rotating vortices. These pylons displayed large amounts of penetration and floor gap. The 1/2-diameter width pylon initially presented the largest flammable fuel plume area (Af), but ceased spreading midway over the cavity. The 4 and 6diameter wide pylons resulted in flow structures dominated by one large set of vortices and displayed minimal penetration. The 6-diameter width pylon fuel plume continued to expand throughout the test section ultimately yielding by far the largest Af. Aerodynamic loses were minimal for all pylon configurations and did not correlate to the size of the pylons tested.

Numerical Study of Hypersonic Wind Tunnel Experiments for Mars Entry Aeroshells

Abstract: The combination of landing future high mass systems with small landing footprints on Mars may require the use of both propulsive deceleration (PD) and reaction control system (RCS) thrusters. However, the interactions between these jets and the supersonic or hypersonic freestream involve complex flow phenomena that are still not well understood. This paper describes numerical and experimental techniques that are used in an effort to develop physically accurate methods to compute these complex flow interactions. The paper also presents a numerical parametric study that is conducted using the computational fluid dynamics (CFD) code LeMANS. This study examines the effects of low temperature and density values and radially nonuniform freestream conditions in the hypersonic wind tunnel facility using an aeroshell based on the Mars Science Laboratory in Mach 12 flow of nitrogen gas with PD and RCS jets off. It is shown that although the Blottner and the Sutherland models compute different values of viscosity at low temperatures, the flowfield and surface properties predicted by LeMANS using these two models are in very close agreement. The study also shows that thermal nonequilibrium effects are negligible. The radial freestream nonuniformities, however, have considerable effects on the flowfield and surface properties. The nonuniform conditions change the temperature and density distributions in most of the computational domain, widen the bow shock around the aeroshell, increase continuum breakdown regions, and decrease the drag coefficient of the capsule compared to the uniform conditions. Finally, the paper presents qualitative experimental comparisons with the computed results which show overall good agreement.

Parametric study of acoustic focusing of particles in a micro-channel in the perspective to improve micro-PIV measurements

Abstract: In this study, we propose a new technique to bring most of the particles in a horizontal plane at mid-height of a micro-channel in order to improve the quality of the micro-PIV measurements. The basic principle is to create a stationary acoustic wave along the channel height so that the resulting acoustic force moves the particles toward the pressure node. A parametric study has been carried out without mean flow to characterize the motion of the particles toward the nodal-plane. We found that focusing speed grows with the acoustic pressure amplitude, with the concentration of particles in the suspension and with the particles diameter. We also led a preliminary investigation of acoustic focusing together with a mean stationary flow. We still observed an important focusing of particles for low freestream velocities. Nevertheless, acoustic focusing is inefficient beyond a given critical freestream velocity U0 for a given set of acoustic parameters and a given type of particles. It was also shown that other phenomena, like clumps formation, can be observed without mean flow if the acoustic focusing lasts long enough.

Analysis of Laminar Falling Film Condensation Over a Vertical Plate With an Accelerating Vapor Flow

Abstract: Laminar falling film condensations over a vertical plate with an accelerating vapor flow is analyzed in this work in the presence of condensate suction or slip effects at the plate surface. The following assumptions are made: (i) laminar condensate flow having constant properties, (ii) pure vapor with a uniform saturation temperature in the vapor region, and (iii) the shear stress at the liquid/vapor interface is negligible. The appropriate fundamental governing partial differential equations for the condensate and vapor flows (continuity, momentum, and energy equations) for the above case are identified, nondimensionalized, and transformed using nonsimilarity transformation. The transformed equations were solved using numerical, iterative, and implicit finite-difference methods. It is shown that the freestream striking angle has insignificant influence on the condensation mass and heat transfer rates, except when slip condition is present and at relatively small Gr l /Re 2 values. Moreover, it is shown that increasing the values of the dimensionless suction parameter (V S ) results to an increase in dimensionless mass of condensate (Γ(L)/(μ l Re)) and Nusselt number (Nu(L)/Re I/2 ). Thus, it results in an increase in condensation mass and heat transfer rates. Finally, it is found that the condensation and heat transfer rates increase as Jakob number, slip parameter, and saturation temperature increase. Finally, the results of this work not only enrich the literature of condensation but also provide additional methods for saving thermal energy.

Collisionless Gas Flows over a Cylindrical or Spherical Object

Abstract: This paper presents exact density, velocity components, and temperature solutions for collisionless gasflows over a cylinder or a sphere. Possible real applications may include collisionless gas flows over a hot wire inside a vacuum chamber and rarefied gasflows aroundanaerosol at veryhigh altitude.At anypoint off the cylinder or the sphere, the local velocity distribution function consists of two pieces ofMaxwellian distribution functions: one for the freestream, which is characterized by the freestream density n0, temperature T0, and velocity U0; the other is characterized by density at the wall nw and wall temperature Tw, where nw is not constant at different surface locations. Directly integrating the distribution functions leads to the detailed flowfield solutions; the solutions are complex but exact.We performed numerical simulationswith the direct simulationMonteCarlomethod to validate these exact solutions. In general, the exact analytical and numerical results are virtually identical.