Free Stream Temperature Research Articles

Hypersonic Boundary-Layer Receptivity over a Blunt Cone to Freestream Pulse Disturbances

Although receptivity plays a key role in the transition of hypersonic flows, most prior computational receptivity studies have neglected to study broadband frequency disturbance spectra. This work uses perfect gas linear stability theory (LST) and direct numerical simulation (DNS) to study the receptivity of flow over a 9.525 mm nose radius, 7 deg half-angle straight cone at Mach 10 using finite spherical and planar pulses to approximate disturbances with broadband frequency spectra. Freestream fast acoustic, slow acoustic, temperature, and vorticity pulses of both geometries were studied to investigate a wide range of forcing conditions. Unsteady DNS predicts second mode growth and agrees well with LST. DNS and LST data are used to extract second mode receptivity coefficients and phase spectra. For the finite pulses the strongest to weakest responses are for the fast acoustic, temperature, slow acoustic, and vorticity pulses, respectively. The planar disturbances show the strongest response for the slow acoustic, temperature, vorticity, and fast acoustic pulses in that order. Fast Fourier transform results show significant variation in the spectral disturbance response between disturbance types and geometries, and the planar fast acoustic pulse in particular is shown to much more readily excite modal disturbances other than the primary second mode.

Effect of Mach number and plate thickness on the flow field and heat transfer characteristics of supersonic turbulent flow over a flat plate at different thermal boundary conditions

Conjugate heat transfer analysis of supersonic turbulent flow over a finite thickness flat plate is studied numerically. The flow field is modeled by employing the Favre averaged Navier–Stokes (FANS) equations. Turbulence is modeled with the Menter’s shear-stress-transport (SST) k−ω model. The comparison of NCHT (non-conjugate heat transfer) and CHT (conjugate heat transfer) analysis shows that the interface temperature and fluid temperature variation for the CHT analysis are lower compared to the NCHT analysis. The results indicate that the interface temperature is significantly increased for the low thermal conductivity plate material, due to the reduced rate of heat transfer. The effect of plate thickness on the flow field temperature variation is negligible. However, it is observed that the maximum interface temperature Ti,max increases with the increase in plate thickness. The values of maximum interface temperature difference between the 5 mm and 2 mm thick Steel-1006 plates at Mach numbers 2, 4, and 5 in non-dimensional (non-dimensionalized with free-stream temperature) form are 0.05594, 0.129, and 0.1816 respectively for the isothermal boundary condition. Results indicate that for Mach 2, the heated wall thermal boundary conditions acts like heat source, leading to the higher interface temperature, whereas for Mach 4, and 5 the heated wall thermal boundary conditions acts like heat sink, thus lowering the interface temperature. The results show that for NCHT analysis the leading edge shock strength, and mean pressure along the wall increases with an increase in Mach number. The non-conjugate results (flow and heat transfer characteristics) of the present numerical study is validated with the direct numerical simulation (DNS) results available in the literature.

Shock interactions in inviscid air and hbox {CO}_2\u2013hbox {N}_2 flows in thermochemical non-equilibrium

The present study aims at providing insights into shock wave interference patterns in gas flows when a mixture different than air is considered. High-energy non-equilibrium flows of air and hbox {CO}_2–hbox {N}_2 over a double-wedge geometry are studied numerically. The impact of freestream temperature on the non-equilibrium shock interaction patterns is investigated by simulating two different sets of freestream conditions. To this purpose, the SU2 solver has been extended to account for the conservation of chemical species as well as multiple energies and coupled to the Mutation++ library (Multicomponent Thermodynamic And Transport properties for IONized gases in C++) that provides all the necessary thermochemical properties of the mixture and chemical species. An analysis of the shock interference patterns is presented with respect to the existing taxonomy of interactions. A comparison between calorically perfect ideal gas and non-equilibrium simulations confirms that non-equilibrium effects greatly influence the shock interaction patterns. When thermochemical relaxation is considered, a type VI interaction is obtained for the hbox {CO}_2-dominated flow, for both freestream temperatures of 300 K and 1000 K; for air, a type V six-shock interaction and a type VI interaction are obtained, respectively. We conclude that the increase in freestream temperature has a large impact on the shock interaction pattern of the air flow, whereas for the hbox {CO}_2–hbox {N}_2 flow the pattern does not change.

Electron heating and cooling in hypersonic flows

Using recently developed advanced numerical methods for plasma flows and sheaths, the first detailed study of electron cooling and heating taking place within hypersonic non-neutral flows is presented here. The numerical simulations fully couple the Navier–Stokes equations for the neutrals to the drift–diffusion model for the electrons and ions and include a 11-species finite-rate chemical solver along with a transport equation for the electron temperature in non-equilibrium. Results for Mach 18 airflow around a wedge with a sharp leading edge show that at low flight dynamic pressure the electron temperature remains close to the freestream temperature in the stagnation region. Such is attributed to the product of the electric field and the electron current being dominantly negative within the plasma sheaths and acting as an electron energy sink. This cooling effect leads to a significant portion of the flow downstream of the shock exhibiting electron temperatures much lower than expected. This study is the first to show a large impact of the non-neutral plasma sheaths on the post-shock electron temperature. This study also shows that the common approach to set the electron temperature equal to the vibrational temperature can result in the electron temperature being over-predicted by one order of magnitude or more in hypersonic flows.

Fully Coupled Turbojet Engine Computational Fluid Dynamics Simulations and Cycle Analyses Along the Equilibrium Running Line

Abstract This work presents fully coupled computational fluid dynamics (CFD) simulations and thermodynamic cycle analyses of a small-scale turbojet engine at several conditions along the equilibrium running line. The CFD simulations use a single mesh for the entire engine, from the intake to the exhaust, allowing information to travel in all directions. The CFD simulations are performed along the equilibrium running line by using the iterative Secant method to compute the fuel flow rate required to match the compressor and turbine power. The freestream pressure and temperature and shaft angular speed are the only inputs needed for the CFD simulations. To evaluate the consistency of the CFD results with thermodynamic cycle results, outputs from the CFD simulations are prescribed as inputs to the cycle model. This approach enables on-design and off-design cycle calculations to be performed without requiring turbomachinery performance maps. In contrast, traditional off-design cycle analyses require either scaling, calculating, or measuring compressor and turbine maps with boundary condition assumptions. In addition, the CFD simulations and the cycle analyses are compared with measurements of the turbojet engine. The CFD simulations, thermodynamic cycle analyses, and measurements agree in terms of total temperature and pressure at the diffuser–combustor interface, air and fuel mass flow rate, equivalence ratio, and thrust. The developed methods to perform CFD simulations from the intake to the exhaust of the turbojet engine are expected to be useful for guiding the design and development of future small-scale gas turbine engines.

Sensitivity Study of Ice Accretion Simulation to Roughness Thermal Correction Model

The effects of atmospheric icing can be anticipated by Computational Fluid Dynamics (CFD). Past studies show that the convective heat transfer influences the ice accretion and is itself a function of surface roughness. Uncertainty quantification (UQ) could help quantify the impact of surface roughness parameters on the reliability of ice accretion prediction. This paper aims to quantify ice accretion uncertainties and identify the key surface roughness correction parameters contributing the most to the uncertainties in a Reynolds-Averaged Navier-Stokes (RANS) formulation. Ice accretion simulations over a rough flat plate using two thermal correction models are used to construct a RANS database. Non-Intrusive Polynomial Chaos Expansion (NIPCE) metamodels are developed to predict the convective heat transfer and icing characteristics of the RANS database. The metamodels allow for the computation of the 95% confidence intervals of the output probability distribution (PDF) and of the sensitivity indexes of the roughness parameters according to their level of influence on the outputs. For one of the thermal correction models, the most influential parameter is the roughness height, whereas for the second model it is the surface correction coefficient. In addition, the uncertainty on the freestream temperature has a minor impact on the ice accretion sensitivity compared to the uncertainty on the roughness parameters.

Hall current impacts on unsteady MHD free convective flow past an infinite vertical porous surface

AbstractIn this paper, the magnetohydrodynamic free convective flow of an incompressible electrically conducting fluid over a vertical plate embedded in a porous medium is considered. A homogeneous transverse magnetic field is applied in the presence of a heat source and chemical reaction in a rotating frame, taking Hall current effects into account. The momentum equations for the fluid flow in a porous medium were determined by Brinkman modeling. At the undisturbed state, both the plate and fluid have an rigid body rotation due to the constant angular velocity, perpendicular to the infinite vertical plane surface. The vertical surface is subject to the homogeneous constant suction and the heat on the surface vary by time about a nonzero constant rate whereas the temperature of free stream is engaged to be constant. The accurate solutions for the velocity, temperature, and concentration distributions were acquired systematically using the perturbation method. The consequences of an assortment of governing flow parameters on the velocity, temperature, and concentration were analyzed through graphical profiles. The computational results for the skin friction, Nusselt number, and Sherwood number in a tabular format were also examined.

Simplified Calibration Method for Constant-Temperature Hot-Wire Anemometry

This study proposes a unique approach to convert a voltage signal obtained from a hot-wire anemometry to flow velocity data by making a slight modification to existing temperature-correction methods. The approach was a simplified calibration method for the constant-temperature mode of hot-wire anemometry without knowing exact wire temperature. The necessary data are the freestream temperature and a set of known velocity data which gives reference velocities in addition to the hot-wire signal. The proposed method was applied to various boundary layer velocity profiles with large temperature variations while the wire temperature was unknown. The target flow velocity was ranged between 20 and 80 m/s. By using a best-fit approach between the velocities in the boundary layer obtained by hot-wire anemometry and by the pitot-tube measurement, which provides reference data, the unknown wire temperature was sought. Results showed that the proposed simplified calibration approach was applicable to a velocity range between 20 and 80 m/s and with temperature variations up to 15 °C with an uncertainty level of 2.6% at most for the current datasets.

Numerical investigation of transient liquid nitrogen cavitating flows with special emphasis on force evolution and entropy features

This study aims to investigate the impacts of thermal effect on cavitation, entropy features and interactions among vorticity, force coefficients and entropy production rate (EPR) in a liquid nitrogen cavitating flow. Numerical results demonstrate that the increase in free-stream temperature intensifies thermal effect and weakens cavitation intensity. The EPR by fluctuating velocity gradient (ṠD'''') dominates the evolution of EPR, and the cavity shedding or collapse increases the velocity gradient, thereby increasing ṠD''''. The variation trend of EPR by wall region (ṠW) is consistent with ṠD''''. By contrast, EPR by temperature gradient (ṠC'''',ṠC¯''') always distributes on the liquid–vapour interface and increases with the development of the attached sheet cavity. Higher temperature acts as a disincentive to each item of EPR. The stable development of negative sheet vorticity at the leading edge increases the force coefficients nearly linearly. The counter clockwise vortex forms at the hydrofoil tail because the small-scale cloud cavity decreases the lift coefficient sharply. As the instability of attached sheet cavity is enhanced by re-entrant jet, the large vortex is dispersed into several clockwise vortexes, and positive vorticity occurs inside the cavity. Consequently, the force coefficients present a downward trend overall with intensive fluctuation. The distribution of EPR is similar to that of vorticity, and the opposite trend of entropy production integral and lift coefficient illustrates that the force can be used as a representation of energy loss to a certain extent.

Mathematical Modeling of Mixed Convection Boundary Layer Flows over a Stretching Sheet with Viscous Dissipation in Presence of Suction and Injection

The variational principle, developed by Gyarmati, embodying the principles of thermodynamics of irreversible processes is employed to study the mixed convection flows near the stagnation point of an incompressible viscous fluid with suction, injection and viscous dissipation effects towards a vertical stretching sheet. The velocity and temperature of the stretching sheet are considered to vary linearly proportional to the distance from the stagnation point. In this analysis, two equal and opposite forces are applied on the stretching sheet by keeping the origin fixed in a viscous fluid with constant free-stream temperature. The velocity and temperature distributions are assumed as simple polynomial functions and then the variational principle has been formulated. The corresponding Euler–Lagrange equations of the variational principle have been transformed into coupled polynomial equations in terms of hydro-dynamical and thermal boundary layer thicknesses. These equations are solvable for any combinations of Prandtl number, suction and injection parameter, Eckert number and buoyancy parameter. The obtained results are compared with known numerical results for assisting and opposing flows, and the comparison reveals that the accuracy is quite acceptable and found to be in good agreement.

Experimental investigation of effusion and transpiration air cooling for single turbine blade

A great number of studies have been conducted on a film cooling for turbine blades, which is to prevent thermal damage on blades originated from high turbine inlet temperature. However, film cooling with several rows of cooling-holes results in lifting-off of coolant film and limited cooling on a restricted area due to flow reattachment. In this study, effusion and transpiration cooling were applied to the single C3X blade. A multiple hole-array with a diameter of 0.5 mm was fabricated by the electric discharging machining, and a porous structure with an equivalent pore diameter of 40 μm was manufactured by the 3-D metal additive manufacturing. Experiments were performed in the high-temperature subsonic wind tunnel, which has a freestream temperature of 100 °C and a velocity of 20 m/s. The surface temperature of blades was measured using infrared thermometry with a specially designed protocol to eliminate background radiation errors from the surroundings. Also, the outflow of coolant from blades was investigated with smoke-laser sheet visualization. The overall cooling effectiveness was quantitatively analyzed on the pressure-side, suction-side, and leading-edge of blades. Due to the enhancement of convective cooling through porous media, transpiration cooling achieves 34% and 25% higher cooling effectiveness than effusion and internal cooling each.

Numerical analysis of an unsteady natural cavitating flow around an axisymmetric projectile under various free-stream temperature conditions

Here, an unsteady natural cavitating flow around an axisymmetric projectile is computationally studied using a homogeneous multiphase approach. The numerical models used are based on a dual-time preconditioning method, an interface-capturing scheme, and a modified cavitation model, to capture unsteady cavitation structure behaviors. Full compressibility of two phases and an energy equation are used to determine the effects of temperature on a cavitating flow. First, the experimental data were validated at a cavitation number of σ = 0.435. Both quantitatively and qualitatively good agreements were achieved, including the evolution of the cavity shape, cavity length, and cavity thickness. Then, the key characteristics of an unsteady cavitation structure regarding the cavity growth, re-entrant jet, cavity shedding, and collapse were analyzed. In particular, the mechanism of the re-entrant jet inside the cavity, causing the periodic cavity shedding, was explored. Furthermore, detailed mechanisms of cavity shedding with periodic cavity–vortex–pressure interaction behaviors were analyzed. Finally, the influences of free-stream temperature on the cavitation structure behaviors were carefully investigated. It was found that both the cavity length and thickness increased with the free-stream temperature under the atmospheric pressure condition. The most sensitive effects occurred when the free-stream temperature approached its boiling point. In case of the same reference cavitation number and Reynolds number, the cavity shape tended to be mushier with increasing water temperature.

Nonlinear dynamics and flutter of plate and cavity in response to supersonic wind tunnel start

The transient response of a plate and a cavity is investigated in a supersonic wind tunnel start experiment where the freestream flow inside the test section reaches turbulent flow at Mach 2. Experimentally measured plate displacement time history shows flutter onset, transition to limit cycle oscillation, and stabilization at a static deformed state during the 30 s run. To analyze and interpret the measured plate response, a fully coupled aero-thermal-acousto-elastic analysis is carried out. A theoretical–computational model is formulated with a nonlinear structural plate model, acoustic pressure equation for the stationary fluid in a cavity, and the first-order Piston Theory aerodynamics. A linear stability analysis is performed that includes the nonlinear added stiffness due to an initial deformation to investigate the combined effects of freestream coupling and temperature differential on system stability. Also, direct time integration of the nonlinear fluid structural equations of motion is performed using experimentally measured flow parameters as inputs. All stability transitions are captured using the theoretical model with good agreement with experiment for transitions from no flutter to flutter/limit cycle oscillations (LCO) although the theoretical LCO amplitude is approximately $$50\%$$ larger than measured. The system’s sensitivity to cavity coupling, temperature differential, thickness calibration, static pressure differential, and turbulent pressure fluctuations are investigated. Lastly, snap-through buckling analyses in response to periodic and quasi-static excitations are conducted.

Numerical investigation on the drag characteristics of supercritical water flow past a sphere

Numerical simulation has become a useful approach to explore the complex physical and chemical process inside the supercritical water (SCW) fluidized bed reactor. Due to the drastic and non-linear variation of water properties near pseudocritical point, the flow field and drag coefficient of SCW flow past a cold particle are considerably different from that of conventional flow. Therefore, in this work, particle-resolved numerical investigation is conducted to study the flow field and drag characteristics under the influence of the special water properties variation. Through varying the enthalpy corresponding to the particle surface temperature, which will be called the particle surface enthalpy for short, in a wide range, it realizes the study under different properties variation tendencies. The simulated results demonstrate that the variations of drag coefficient versus Reynolds number (Re) and particle surface enthalpy are in good regularity when taking the freestream temperature as reference temperature. The drag coefficient is enhanced greatly at high enthalpy difference between particle surface and inflow, and the enhancement is mainly contributed by that of the frictional drag coefficient. Moreover, the drag coefficient variations under different pressures are in good agreement when cases are set with the same inflow and particle surface enthalpies, respectively. By fitting the simulated results, a new drag coefficient correlation is developed for Re range of 10–200 with consideration of the influence of the special properties variation. The fitting quality is good that the maximum deviation between the new correlation and simulated data is 13.92%, and the mean deviation is 3.67%.

Low cost thermal transient anemometer for challenging gas flow rate measurements

Few commercially available gas flow rate measurement devices can be employed in applications with strict pressure drop allowances, high working pressures, or corrosive working fluids. Additionally, most measurement approaches (e.g., turbine, rotameter, thermal dispersion) have limited turn-down ratios, generally less than 50. Here, a new economical and mechanically simple thermal transient anemometer design is proposed and evaluated for internal gas volumetric flow measurement. The flow meter operates through cyclical electrical heating and convective cooling of a thermocouple probe. Flow rates are correlated with average cooling-period temperatures. Heating and cooling profiles are dynamically adjusted during operation, permitting relatively good accuracy and a large turn-down ratio (450). The objective of this investigation is to model, design, and demonstrate the operation of the anemometer using air as working fluid. The anemometer has a measurement range of 0.5–226.5 l min−1 with free stream temperatures varying between 22–26°C. A segmented numerical model, which includes the varying heating loads and velocity profiles in the working fluid, is developed and validated.

Double-diffusive natural convection in a solar distiller with external fluid stream cooling

Numerical results of laminar double-diffusive natural convection in a trapezoidal shape solar distiller occupied with an air-vapor mixture are carried out. In the present paper, the distiller is subjected to cooling fluid with a cold free stream temperature from the upper wall that kept at low concentration. The lower distiller wall kept with hot temperature and high concentration. The finite volume method based on SIMPLE algorithm is employed to solve the governing equations. Outcomes are performed with a scope of Rayleigh number (104 ≤ Ra ≤ 106), free stream Reynolds number (102 ≤ Re∞ ≤ 105), buoyancy ratio (N = 1, 2,5 and 10) and varying cooling fluid (air or water). The Prandtl (Pr), Schmidt (Sc) and Lewis (Le) numbers are fixed at 0.7, 0.62 and 0.89, respectively. The results revealed a considerable enhancement on the mass and heat transfer rates with increasing of Ra, N and Re∞. The effect of Re∞ is more pronounced with Ra = 106. On the other hand, more vortices formed in the cavity as Ra and N augments and the maximum vortices number obtained when N = 5. Regarding the local Nusselt (NuL) and Sherwood (ShL) numbers, improvements are found both on the upper and lower cavity walls as Ra and N rise. The impact of N on NuL and ShL turns out significant with the higher value (N = 10).

Liquid-Fuel Injection into Supersonic Cross Flow

ABSTRACT An experimental observation of kerosene injected into supersonic flow is presented. A reflected shock tunnel is used to produce high-temperature Mach 2 airflow. A flat plate injector model with a 0.5 mm orifice is installed at the tunnel nozzle exit. The liquid injection velocity is controlled from 47 m/s to 61 m/s. A high-speed schlieren system is used to observe the jet breakup and mixing phenomena. Schlieren observations show that the bow shock/boundary separation shock interactions have a significant effect on the spray dissipation. The interactions induce a strong spray whipping motion, causing droplet dispersion from the concentrated spray cone and quick vaporization into the airflow. The dispersed droplets also interact with the large eddy structures on the spray cone surface; a series of schlieren images shows the development of eddy structures, and their dissipation distances are closely related to the jet-to-freestream momentum ratio, J. Increasing J enhances the instability of the spray cone and decreases its dissipation distance. A Mie scattering system is also used to characterize the spray. Side-view and top-view Mie scattering images of the spray are captured by an intensified-CCD camera. The top view Mie scattering images of the spray at different heights from the wall also show the formation of vortices and the whipping motion of the spray caused by shock/shock interaction. To characterize the droplet dissipation distance, 100 schlieren images were averaged. The image was pseudo-colored to indicate the spray boundary, and this was used to identify the penetration height and spray dissipation distance. The local vertical peak of the schlieren intensity was identified. Based on the distribution of the peaks, the layers of droplet evaporation and gas-phase mixing zones could be recognized, and the penetration heights and dissipation distance of the spray identified. The trajectory relation of momentum flux ratio and penetration height is also presented in this paper, meeting the need for experimental data on penetration height of liquid jets in high-temperature supersonic flows. The penetration height results in this study are lower than those of Lin, perhaps due to differences in free stream temperature and measuring technique.

A theoretical computational model of a plate in hypersonic flow

A theoretical model of an elastic panel in hypersonic flow is derived to be used for design and analysis. The nonlinear von Kármán plate equations are coupled with 1st order Piston Theory and linearized at the nonlinear steady-state deformation due to static pressure differential and thermal loads. Eigenvalue analysis is applied to determine the system’s stability, natural frequencies and mode shapes. Numerically time marching the equations provides transient response prediction which can be used to estimate limit cycle oscillation amplitude, frequency and time to onset. The model’s predictive capability is assessed by comparison to an experiment conducted at a free stream flow of Mach 6. Good agreement is shown between the theoretical and experimental natural frequencies and mode shapes of the fluid–structure system. Stability analysis is performed using linear and nonlinear methods to plot stability, flutter and buckling zones on a free stream static pressure vs temperature differential plane.

Analysis of frost thickness and roughness growth from the perspective of frost crystal structure

Laboratory experiments were conducted to characterize frost thickness and roughness on a horizontal cold flat surface with respect to the type of frost crystal. Air velocities, free stream temperatures, wall temperatures, and relative humidities were varied from 0.5 to 1.5 m s−1, 16 to 6 °C, and -25 to −15 °C, and 50 to 75%, respectively. Three-dimensional photogrammetry was employed for evaluating frost roughness characteristics. The results showed that the frost growth corresponded with changes of frost crystal formation. Feather and needle crystals created a thick and porous layer with a rough surface, while flake and irregular crystals formed a thin and dense frost layer with a relatively smooth surface. Frost root-mean-square height began to decrease sooner under higher air velocities, higher air temperatures, and higher wall temperatures. The maximum value of frost root-mean-square height was largest under lower air velocities, lower air temperatures, lower wall temperatures, and higher relative humidities. Larger frost surface skewness occurred under lower air velocities, lower air temperatures, higher wall temperatures, and higher relative humidities. The impacts of increasing relative humidity on the frost roughness parameters plateaued at higher relative humidities.

Uncertainty and sensitivity analysis of inflow parameters for HyShot II scramjet numerical simulaiton

The flowfield inside a combustor of scramjet such as Hyshot II system is highly complicated and many factors have effect on its numerical prediction. Uncertainty and sensitivity analysis of aerodynamics prediction on Hyshot II intake configuration is performed in this work. The inflow conditions of intake configuration are of vital crucial since they directly determine the inflow conditions of combustor configuration, which in turn have a remarkable influence on the combustion and mixing process. Meanwhile, the varied flight conditions may also introduce great and direct impact on the performance in actual flight tests. It is significant to evaluate the uncertainties and sensitivities and to identify the critical factors of inflow conditions for the intake configuration. Five input parameters are selected as the epistemic uncertain variables. The flowfield prediction is conducted via using Reynolds-averaged Navier-Stokes simulations as the numerical study approach with standard Menter's shear stress transport turbulence model and species transport process for Hyshot II configuration. Stochastic expansions based on point collocation non-intrusive polynomial chaos, which require 42 deterministic simulations in this study, are employed to propagate and estimate the uncertainties. Meanwhile, Sobol indices are adopted to rank and indicate the individual contribution and to identify the critical inflow parameters. The results demonstrate that freestream Mach number and temperature are the dominated contributing parameters among the performance parameters. In addition, as observed from the wall-normal profile of related variables extracted at 355 mm in x coordinate direction in the simulation results, the freestream pressure plays a dominant role in determining the pressure distribution and the freestream temperature is the most prominent contributor to the distribution of temperature and velocity.