Freestream Value Research Articles

Influence of the tip speed ratio on the wake dynamics and recovery of axial-flow turbines

Detached eddy simulation is employed to investigate the wake development downstream of the rotor of an axial-flow turbine and its dependence on the tip speed ratio. In this study, we found that the trend of the momentum deficit as a function of the rotational speed shows opposite directions in the near wake and further downstream. While the momentum deficit in the near wake increases with the rotational speed, it decreases further downstream. For instance, we found that at six diameters downstream of the rotor the streamwise velocity in its wake recovered to about 30% of its free-stream value at the lowest simulated tip speed ratio of 4, while its recovery was equal to about 65% at the largest tip speed ratio of 10. This is due to the earlier breakdown of the tip vortices. The results of the computations demonstrate indeed that mutual inductance phenomena between tip vortices, promoting pairing events and the eventual instability of the helical structures, occur at shorter downstream distances for higher values of tip speed ratio. Wake instability enhances the process of wake recovery, especially due to radial advection. Therefore, higher rotational speeds do not promote wake recovery through more intense tip vortices, but through their greater instability. Implications are important, affecting the optimal distance between rows of axial-flow turbines in array configurations: the operation at higher rotational speeds allows for smaller distances between turbines, decreasing the cost and environmental impact of farms consisting of several devices.

Interrelationships of entropy production and turbulence kinetic energy associated with simple angle and compound angle full coverage film cooling

The present paper compares experimentally-measured distributions of entropy generation with numerically-predicted distributions of streamwise vorticity, turbulence kinetic energy, and production of turbulence kinetic energy. These comparisons are provided for two full-coverage film cooling environments which are designed to model the thermal management arrangements employed for combustor liners within gas turbine engines. One of these arrangements includes alternating compound angle values of +30° in one row of holes, followed by −30° in the next row of holes. The other arrangement includes simple angle holes with a zero degree compound angle value. The associated full-coverage film cooled boundary layers are investigated within a double-wall cooling test facility wherein the air for each full-coverage film cooling arrangement is provided by an impingement jet array. Experimentally-measured entropy generation values are obtained from film cooled boundary layer measurements of local total pressure variations, obtained in isothermal flow, relative to the freestream values outside of the boundary layer. The resulting entropy generation values quantify second law losses, which are associated with aerodynamic gains. To obtain the associated numerical-prediction results for a steady-state, three-dimensional flow field, employed is the ANSYS FLUENT Version 2022 R2 computational code with a SST k–ω turbulence closure model. The resulting comparisons of entropy generation, streamwise vorticity, turbulence kinetic energy, and production of turbulence kinetic energy are provided for a blowing ratio BR of 2.9 for simple angle film cooling with a main flow Reynolds number Rems of 138,000, and for compound angle film cooling with a main flow Reynolds number Rems of 142,000. Overall, evidence is provided of strong relationships between local turbulence kinetic energy and local entropy production since the two quantities are highly correlated with each other over s substantial range of experimental conditions and configurations. For example, ratio of turbulence kinetic energy to entropy generation data collapse for Z/de values from 0 to 3.5 for Y/de = 0.5, Y/de = 1.5, and both film cooling arrangements. Here, the value of the TKE/Sgen ratio is approximately constant for these conditions, which evidences direct and simple dependences of local turbulence kinetic energy upon local entropy generation, even for lower magnitudes of Z/de. The direct and simple dependences of local turbulence kinetic energy upon local entropy generation are further illustrated by the simplicity of linear correlation equations, which represent physical behavior for different conditions and configurations. These correlation equations are developed for three arrangements, which are associated with X/de = 54.54.

Collisionless Accretion onto Black Holes: Dynamics and Flares.

We study the accretion of collisionless plasma onto a rotating black hole from first principles using axisymmetric general-relativistic particle-in-cell simulations. We carry out a side-by-side comparison of these results to analogous general-relativistic magnetohydrodynamic simulations. Although there are many similarities in the overall flow dynamics, three key differences between the kinetic and fluid simulations are identified. Magnetic reconnection is more efficient, and rapidly accelerates a nonthermal particle population, in our kinetic approach. In addition, the plasma in the kinetic simulations develops significant departures from thermal equilibrium, including pressure anisotropy that excites kinetic-scale instabilities, and a large field-aligned heat flux near the horizon that approaches the free-streaming value. We discuss the implications of our results for modeling event-horizon scale observations of Sgr A* and M87 by GRAVITY and the Event Horizon Telescope.

Flat Unglazed Transpired Solar Collector: Performance Probability Prediction Approach Using Monte Carlo Simulation Technique

Engineering applications including food processing, wastewater treatment, home heating, commercial heating, and institutional heating successfully use unglazed transpired solar collectors (UTCs). Trapping of solar energy is the prime goal of developing an unglazed transpired solar collector. The UTC is usually developed in and around the walls of the building and absorbs the solar energy to heat the air. One of the key challenges faced by the UTC designer is the prediction of performance and its warranty under uncertain operating conditions of flow variables. Some of the flow features are the velocity distribution, plate temperature, exit temperature and perforation location. The objective of the present study was to establish correlations among these flow features and demonstrate a method of predicting the performance of the UTC. Hence, a correlation matrix was generated from the dataset prepared after solving the airflow over a perforated flat UTC. Further, both strong and weak correlations of flow features were captured through Pearson’s correlation coefficient. A comparison between the outcomes from a linear regression model and that of computational simulation was showcased. The performance probability for the UTC was interlinked with correlation matrix data. The Monte Carlo simulation was used to predict the performance from random values of the flow parameters. The study showed that the difference between the free stream value of temperature and the value of temperature inside the UTC’s chamber varied between 15 and 20 °C. The probability of achieving system efficiency greater than 35% was 55.2%. This has raised the hope of recommending the UTC for drying and heating where the required temperature differential is within 20 °C.

The Application of the γ-Reθt Transition Model Using Sustaining Turbulence

The freestream turbulence intensity is an important parameter for Tollmien–Schlichting waves and is also used as one of the key variables for the local- and transport-equation-based transition model in the simulations. To obtain the similar turbulence level in the vicinity to the aircraft as the turbulence intensity measured in a wind tunnel or in free-flight conditions, the sustaining turbulence term can be used for the transition model. It is important to investigate the model behavior when the sustaining turbulence is coupled with the frequently used SST-variants for transitional flows. Additionally, it is essential to obtain a nearly independent solution using the same transition model for different users on different meshes with similar grid resolution for purposes of verification and validation. So far, the relevant work has not been performed sufficiently and the sustaining turbulence technology introduces non-independent results into the freestream values. Thus, a modified sustaining turbulence approach is adopted and investigated in several test cases, including a computational effort on NACA0021 test case at 10 angles of attack. The results indicate that the modified sustaining turbulence in conjunction with the SST-2003 turbulence model yields results nearly independent to the freestream value of ω for the prediction of both streamwise and crossflow transition for two-dimensional flows without increasing computational effort too much. For three-dimensional flow, the sensitivity to initial value of ω is reduced significantly as well in comparison to the SST-based transition model, and it is highly recommended to use present sustaining turbulence technology in conjunction with the SST-2003-based transition model for engineering applications.

Flow around the wing models with straight and swept leading edge in case of contact with turbulent wake

The paper presents the results of experimental studies of the flow around wing models with a straight and swept leading edge in contact with a turbulent wake. The experiments were carried out in subsonic wind tunnels at low Reynolds numbers. A fluffy thread was used to simulate a turbulent wake in the flow. The flow patterns on the surface of the wings were obtained before and after the impact of the turbulent wake at various angles of attack, wing sweep angles and free-stream velocity values. It was found that the wake has a significant effect on flow separation and on vortex structures arising above the wings. The evolution of the vortex flow patterns in the areas of separation of the boundary layer and with a change in the flow regime is shown.

Non-equilibrium effects on flow past a circular cylinder in the slip and early transition regime

This paper presents a comprehensive investigation into flow past a circular cylinder where compressibility and rarefaction effects play an important role. The study focuses on steady subsonic flow in the Reynolds-number range 0.1–45. Rarefaction, or non-equilibrium, effects in the slip and early transition regime are accounted for using the method of moments and results are compared to data from kinetic theory obtained from the direct simulation Monte Carlo method. Solutions obtained for incompressible continuum flow serve as a baseline to examine non-equilibrium effects on the flow features. For creeping flow, where the Reynolds number is less than unity, the drag coefficient predicted by the moment equations is in good agreement with kinetic theory for Knudsen numbers less than one. When flow separation occurs, we show that the effects of rarefaction and velocity slip delay flow separation and will reduce the size of the vortices downstream of the cylinder. When the Knudsen number is above 0.028, the vortex length shows an initial increase with the Reynolds number, as observed in the standard no-slip continuum regime. However, once the Reynolds number exceeds a critical value, the size of the downstream vortices decreases with increasing Reynolds number until they disappear. An existence criterion, which identifies the limits for the presence of the vortices, is proposed. The flow physics around the cylinder is further analysed in terms of velocity slip, pressure and skin friction coefficients, which highlights that viscous, rarefaction and compressibility effects all play a complex role. We also show that the local Knudsen number, which indicates the state of the gas around the cylinder, can differ significantly from its free-stream value and it is essential that computational studies of subsonic gas flows in the slip and early transition regime are able to account for these strong non-equilibrium effects.

Wave Generation and Heat Flux Suppression in Astrophysical Plasma Systems

Abstract Heat flux suppression in collisionless plasmas for a large range of plasma β is explored using two-dimensional particle-in-cell simulations with a strong, sustained thermal gradient. We find that a transition takes place between whistler-dominated (high-β) and double-layer-dominated (low-β) heat flux suppression. Whistlers saturate at small amplitude in the low beta limit and are unable to effectively suppress the heat flux. Electrostatic double layers (DLs) suppress the heat flux to a mostly constant factor of the free-streaming value once this transition happens. The DL physics is an example of ion–electron coupling and occurs on a scale of roughly the electron Debye length. The scaling of ion heating associated with the various heat flux driven instabilities is explored over the full range of β explored. The range of plasma-βs studied in this work makes it relevant to the dynamics of a large variety of astrophysical plasmas, including the intracluster medium of galaxy clusters, hot accretion flows, stellar and accretion disk coronae, and the solar wind.

Numerical Analysis of Flow Around Bluff Bodies with 4th and 2nd order compact formulations

In the present study, fourth-order compact formulation has been improved for Navier-Stokes (N-S) equations, which is expressed for two-dimensional, steady, incompressible flow problems. N-S equation system has been expressed with Stream Function-Vorticity Approach using Finite Difference Method (FDM) from the numerical methods. In order to test the functionality and applicability of the improved numerical formulation, a sample for submerged bluff bodies, flow problem around cylinder with square cross-section was chosen as a benchmark problem. As a result of applying improved numerical formulation with Gauss-Seidel Relaxation Method was used for this benchmark problem. The benchmark problem was also solved with second-order accuracy and obtained numerical results were compared with fourth-order accuracy numerical results. With the same Reynolds Number and the same free-stream velocity values, fourth-order numerical results are more convergent than second-order numerical results. Furthermore, in the flow field for considered benchmark problem, separation bubble length that consisted in the wake region is increased proportionally depending on the alteration of the Reynolds Number values.

Flux-Line Theory: A Novel Analytical Model for Cycloturbines

In this paper, a novel low-order blade element momentum model, called flux-line theory, is developed for predicting the performance of cycloturbines (variable-pitch vertical-axis wind turbines). It improves upon prior momentum theories by capturing flow expansion/contraction and bending through the turbine. This is accomplished by performing fluid calculations in a coordinate system fixed to streamlines for which the spatial locations are not predescribed. A transformation determines the Cartesian location of streamlines through the rotor disk, and additional calculations determine the power and forces produced. Validations against three sets of experimental data demonstrate improvement over other existing streamtube models. An extension of the theory removes dependence on a blade element model to better understand how turbine–fluid interaction impacts power production. A numerical optimization and simplified analytical analysis identify that maximum power (for a turbine that exclusively decelerates the flow) is produced when the upstream portion of the rotor does not interact with the flow, whereas the downstream portion of the turbine decelerates the flow by just over one-third of the freestream value. The theoretical power coefficient limit falls in a range below 0.8, depending on the prescription of the submodel describing the angle at which the flow crosses the blade path (0.597 for the best-fit model). A larger effective turbine area explains the higher-than-Betz limit result.

Prospects for generating electricity by large onshore and offshore wind farms

The decarbonisation of energy sources requires additional investments in renewable technologies, including the installation of onshore and offshore wind farms. For wind energy to remain competitive, wind farms must continue to provide low-cost power even when covering larger areas. Inside very large wind farms, winds can decrease considerably from their free-stream values to a point where an equilibrium wind speed is reached. The magnitude of this equilibrium wind speed is primarily dependent on the balance between turbine drag force and the downward momentum influx from above the wind farm. We have simulated for neutral atmospheric conditions, the wind speed field inside different wind farms that range from small (25 km2) to very large (105 km2) in three regions with distinct wind speed and roughness conditions. Our results show that the power density of very large wind farms depends on the local free-stream wind speed, the surface characteristics, and the turbine density. In onshore regions with moderate winds the power density of very large wind farms reaches 1 W m−2, whereas in offshore regions with very strong winds it exceeds 3 W m−2. Despite a relatively low power density, onshore regions with moderate winds offer potential locations for very large wind farms. In offshore regions, clusters of smaller wind farms are generally preferable; under very strong winds also very large offshore wind farms become efficient.

UNSTEADY HYDROMAGNETIC HEAT AND MASS TRANSFER NATURAL CONVECTION FLOW PAST AN EXPONENTIALLY ACCELERATED VERTICAL PLATE WITH HALL CURRENT AND ROTATION IN THE PRESENCE OF THERMAL AND MASS DIFFUSIONS

In the present analytical study, we have considered unsteady hydromagnetic heat and mass transfer natural convection flow of an electrically conducting, heat absorbing and chemically reacting fluid past an exponentially accelerated vertical plate in a uniform porous medium taking Hall current and rotation into account. The species concentration near the plate is considered to be varies linearly with time. Two particular cases for plate temperature are considered i.e. (i) plate temperature is uniform and (ii) plate temperature varies linearly with time and after some time it is maintained at uniform temperature. The coupled partial differential equations governing the fluid flow problem are solved analytically for fluid velocity, temperature and species concentration using Laplace transform method. To examine the physical characteristic of this problem the graphs for velocity, temperature, species concentration, skin friction, Nusselt number and Sherwood number distributions are computed and generated for various values of different pertinent flow parameters. It is observed that for small thermal diffusion, the free stream value of velocity and temperature are achieved nearer to the plate in comparison to that for large thermal diffusion.

Open water bells

A smooth circular moving liquid sheet is formed by the head-on impingement of two equal laminar water jets. We subject such a liquid sheet to uniform laminar air flow from one side such that the direction of air velocity is perpendicular to the liquid sheet. The pressure of the moving air deforms the liquid sheet giving rise to an open water bell. The water bell is symmetric suggesting that the gas flow around the bell is also symmetric and that the gravitational force is negligible. We have captured the shape of the water bells for varying air flow rates and for varying Weber numbers, and compared the measurements with theoretical predictions obtained from a force balance involving liquid inertia, surface tension, and pressure difference across the sheet. The pressure exerted by the gas phase on the front and the rear surface of the deformed liquid sheet is obtained from known results of flow past flat circular discs. The predicted steady state shapes match well with the measurements at low Weber numbers but differences are observed at high Weber numbers, where the sheet flaps and is no longer smooth. Interestingly, the shape predicted by assuming a constant pressure difference equal to the stagnation pressure over the whole of the front face of the sheet and free stream value over the whole of the rear face yields nearly identical results suggesting that an open water bell is similar to a closed water bell in that, to a good approximation, the pressure on either sides of the water bell is homogeneous.

Characterization of CO2 flow in a hypersonic impulse facility using DLAS

This work documents diode laser absorption measurements of CO2 flow in the free stream of the Longshot hypersonic impulse facility at Mach numbers ranging from 10 to 12. The diode laser sensor was designed to measure absorption of the P12 (30013) \(\leftarrow\) (00001) transition near 1.6 \(\upmu\)m, which yields relatively weak direct absorption levels (3.5 % per meter at peak Longshot free-stream conditions). Despite this weak absorption, measurements yielded valuable flow property information during the first 20 ms of facility runs. Simultaneous measurements of static temperature, pressure, and velocity were acquired in the inviscid core flow region using a laser wavelength scanning frequency of 600 Hz. The free-stream values obtained from DLAS measurements were then compared to Longshot probe-derived values determined from settling chamber and probe measurements. This comparison enabled an assessment of the traditional method of flow characterization in the facility, which indicated negligible influence from possible vibrational freezing of reservoir gases.

Characterization of wind velocities in the upstream induction zone of a wind turbine using scanning continuous-wave lidars

As a wind turbine generates power, induced velocities, lower than the freestream velocity, will be present upstream of the turbine due to perturbation of the flow by the rotor. In this study, the upstream induction zone of a 225 kW horizontal axis Vestas V27 wind turbine located at the Danish Technical University's Risø campus is investigated using a scanning Light Detection and Ranging (lidar) system. Three short-range continuous-wave “WindScanner” lidars are positioned in the field around the V27 turbine allowing detection of all three components of the wind velocity vectors within the induction zone. The time-averaged mean wind speeds at different locations in the upstream induction zone are measured by scanning a horizontal plane at hub height and a vertical plane centered at the middle of the rotor extending roughly 1.5 rotor diameters (D) upstream of the rotor. Turbulence statistics in the induction zone are studied by more rapidly scanning along individual lines perpendicular to the rotor at different radial distances from the hub. The mean velocity measurements reveal that the longitudinal velocity reductions become greater closer to the rotor plane and closer to the center of the rotor. Velocity deficits of 1%–3% of the freestream value were observed 1 D upstream of the rotor, increasing at the rotor plane to 7.4% near the edge of the rotor and 18% near the center of the rotor while the turbine was operating with a high estimated mechanical coefficient of power (CP) of 0.56 yielding an estimated axial induction factor of 0.25. The velocity reductions relative to the freestream velocity become smaller when the turbine's coefficient of power decreases; for a low CP of 0.16 resulting in an estimated induction factor of 0.04, the velocity deficits are ∼1% of the freestream value 1 D upstream of the rotor and only 6% at the rotor plane near the center of the rotor. Additionally, the mean radial wind speeds were found to increase close to the edge of the rotor disk indicating an expansion of the incoming flow around the rotor. Radial velocity magnitudes at the edge of the rotor disk of approximately 9% and 3% of the freestream longitudinal wind speed were measured for the abovementioned high and low CP values, respectively. Turbulence statistics, calculated using 2.5-min time series, suggest that the standard deviation of the longitudinal wind component decreases close to the rotor, while the standard deviation of the radial wind component appears to increase. When the turbine was operating with a high CP of 0.54 resulting in an estimated induction factor of 0.22, standard deviation decreases of up to 22% of the estimated freestream value and increases of up to 46% were observed for the longitudinal and radial components, respectively, near the center of the rotor.

Non-Uniform Nozzle Flow Heat Exchange Effects

Considering boundary layer effects in one-dimensional flow with heat exchange, true mean value flow parameters and their ratio to uniform free-stream values are derived. For one seventh power velocity distribution law and similar stagnation temperature and profiles variation in Mach number, stagnation temperature and impulse at the exit section are plotted versus boundary layer thickness.

Analytical Solution for the Optimal Spacing of Wind Turbines

The lateral and longitudinal spacing between individual turbines in a wind turbine array must be large enough to minimize the wake effects caused by an upstream turbine on those that lie downstream from it. Here, the flow downstream of a single wind turbine is examined by modeling its far-field development as a turbulent axisymmetric wake which is well described in the turbulence literature. In particular, the velocity defect profile in the wake is approximated by a Gaussian function in the radial coordinate. Scaling laws are used to derive closed-form solutions for the wake diameter, wake velocity defect, and wake power recovery as functions of downstream distance from the rotor. Our results show that at a downstream distance of 10 rotor diameters, the wake centerline velocity will recover to 77% of the free-stream value. It is also seen that the power within the wake recovers quickly for small downstream distances, but beyond about 10 rotor diameters, the rate of power recovery slows down. Implications for the optimal spacing of wind turbines are discussed based on these findings.

ELECTRON HEAT CONDUCTION IN THE SOLAR WIND: TRANSITION FROM SPITZER-HÄRM TO THE COLLISIONLESS LIMIT

We use a statistically significant set of measurements to show that the field-aligned electron heat flux $q_\parallel$ in the solar wind at 1 AU is consistent with the Spitzer-H\"{a}rm collisional heat flux $q_{sh}$ for temperature gradient scales larger than a few mean free paths $L_T \gtrsim 3.5 ~\lambda_{fp}$. This represents about 65% of the measured data and corresponds primarily to high $\beta$, weakly collisional plasma ('slow solar wind'). In the more collisionless regime $\lambda_{fp}/L_T \gtrsim 0.28$, the electron heat flux is limited to $q_\parallel/q_0 \sim 0.3$, independent of mean free path, where $q_0$ is the 'free-streaming' value; the measured $q_\parallel$ does not achieve the full $q_0$. This constraint $q_\parallel/q_0 \sim 0.3$ might be attributed to wave-particle interactions, an interplanetary electric potential, or inherent flux limitation. We also show a $\beta_e$ dependence to these results that is consistent with a local radial electron temperature profile $T_e \sim r^{-\alpha}$ that is a function of the thermal electron beta $\alpha = \alpha(\beta_e)$ and that the $\beta$ dependence of the collisionless regulation constraint is not obviously consistent with a whistler heat flux instability. We discuss the results in a broader astrophysical context.

Influence of Turbulence Intensities onto Transmission Line Conductor Wind Loads

The rationality of transmission line responses, tower responses, etc., are determined by the computed wind loads, which are directly correlated with the free-stream turbulences that generated at different ground roughness conditions, different terrains, etc.. Accounting for this problem, the flow fields around transmission line conductor LGJ630/45 are computed by solving Navier-Stokes equations to study the influence of Tis (turbulence intensities) onto wind load characteristics. The results show that, the peak-values of power spectrum density (PSD) results of both lift and drag are obviously influenced by TIs, while their corresponding frequencies are kept the same at different TIs; with the increase of Tis, the time-averaged value of conductor drag decreases nonlinearly and monotonically. Thus, given the influence of TIs onto wind loads, field observed free-stream values should be used as inputs for numerical simulations, and then the obtained wind loads can be adopted to accurately simulate transmission line gallopings and windage yaws.

The modification of wind turbine performance by statistically distinct atmospheric regimes

Power production from wind turbines can deviate from the manufacturer’s specifications due to variability in atmospheric inflow characteristics, including stability, wind shear and turbulence. The practice of insufficient data at many operational wind farms has made it difficult to characterize this meteorological forcing. In this study, nacelle wind measurements from a wind farm in the high plains of central North America were examined along with meteorological tower data to quantify the effects of atmospheric stability regimes in the boundary layer on turbine power generation. The wind power law coefficient and the bulk Richardson number were used to segregate time periods by stability to generate regime-dependent power curves. Results indicated underperformance during stable regimes and overperformance during convective regimes at moderate wind speeds (8–12 m s−1). Statistical testing using the Monte Carlo approach demonstrated that these results were robust, despite potential deviations of the nacelle wind speeds from free-stream inflow values due to momentum loss from the turbine structure and spinning rotor. A hypothetical stability dependence between free-stream and nacelle wind speeds was generated that can be evaluated in future analyses. The low instrumentation requirement of our power analysis technique should enable similar studies at many wind sites formerly considered inappropriate.