Static Pressure Taps Research Articles

Effects of Perforated Plates on Shock Structure Alteration for NACA0012 Cascade Configurations

To alleviate the shock boundary layer interaction adverse effects, various active or passive flow control strategies have been investigated in the literature. This research sheds light on the behavior of perforated plates as passive flow control techniques applied to NACA0012 airfoils in cascade configurations. Two identical perforated plates with shallow cavities underneath are accommodated on the upper and lower surfaces of each airfoil in the cascade arrangement. Six different cascade arrangements, including a baseline configuration with no control applied, are additively manufactured, with different perforated plate orifice sizes in the range of 0.5–1.2 mm. A high-speed wind tunnel with Schlieren optical diagnosis and wall static pressure taps is used to investigate the changes in the shock waves pattern triggered by the perforated plates. Steady 3D density-based numerical simulations in Ansys FLUENT are conducted for further analysis and validation. In the cascade configuration, the perforated plates alter the shock structure, and the strong normal shock wave is replaced by a weaker X-type shock structure. Eventually, a 1% penalty in overall total pressure loss is induced by the perforated plates because of the negative loss balance between the reduced shock losses and the enhanced viscous losses. Further studies on perforated plate geometrical features are needed to improve this outcome in a cascade arrangement.

Experimental test of a compressor cascade with non-axisymmetric end-wall contouring at off-design conditions

End-wall losses in axial flow turbomachinery, particularly in compressors, constitute a significant challenge due to their adverse impact on overall efficiency. Pioneering works in this field have demonstrated the potential for end-wall loss reduction by improving end-wall profiles. However, many previous efforts have concentrated solely on design conditions, largely disregarding the behavior of these contoured end-walls under off-design conditions—where compressors often operate. This study investigates the adaptability of a non-axisymmetric end-wall contour, performing well under design conditions, to off-design scenarios, focusing particularly on the influence of Mach numbers on its ability to control corner separation effects. Experimental research was conducted using a combination of surface static pressure taps and aerodynamic probes to quantitatively and qualitatively analyze the effect of the non-axisymmetric end-wall contour on reducing losses. Quantitative outcomes demonstrate a notable decrease in overall losses in the blade cascade due to this end-wall contour. For all tested Mach numbers, the average loss reduces by 4% at 0 degrees of incidence, with a 0.9° decrease in deviation angle, and an 8% average loss reduction at 5 degrees of incidence, accompanied by a 1.5° decrease in deviation angle. Qualitative findings suggest that the mechanism by which the non-axisymmetric end-wall contour reduces blade cascade losses involves the enhancement of pitchwise pressure gradients. This enhancement redirects low-momentum fluid toward the blade's suction surface, diminishing its reach in the pitchwise direction. However, it also intensifies loss in the low-momentum fluid core. Additionally, the presence of a convex feature in the rear section of the blade passage mitigates pitchwise static-pressure gradients, effectively ameliorating secondary flows and preventing their further decline. Moreover, it was observed that the control effectiveness of the end-wall contour on corner separation increases with higher Mach numbers.

Investigation of the supersonic flow past a wedge-shaped geometry using pressure sensitive paints technique

This study aims to present results of an investigation of the supersonic flow past a wedge-shaped geometry using the pressure sensitive paints technique (PSP). The wedge-shaped geometry was chosen as a canonical case for the investigation of the supersonic flow involving shock waves and strong expansion making it a convenient case to build a first practical experience with this technique, further intended for use in the investigation of linear blade cascades in high speed laboratory of the Institute of Thermomechanics of the Academy of Sciences of the Czech Republic. The tests on the wedge-shaped geometry were complemented with the numerical simulations and static pressure taps measurements. The resulting static pressure distribution obtained using the PSP on the wedge-shaped model revealed all main flow structures including positions of the separation and reattachment shocks providing a good picture of the whole flow field.

Leading-Edge Active Flow Control Enabled by Curved Fluidic Oscillators

A new design of fluidic oscillator, in which the oscillator is curved along its primary flow direction, allows for a sweeping jet to be placed near the leading edge of a wing as an active flow control device. Previous studies of fluidic oscillator applications have shown their promise as an active flow control device by increasing the lift over a wing and preventing flow separation. However, the planar extent of the flat fluidic oscillators creates challenges when trying to optimally implement them in a confined geometry. The application of these new curved oscillators is experimentally investigated on the leading edge of an upswept NACA0018 airfoil full-span wing. Global load cell measurements of lift, drag, and pitching moment are presented and analyzed using suction surface static pressure taps, and particle image velocimetry data are presented. The effects of active flow control on lift, drag, and stall at a Reynolds number of 100,000 are documented for a variety of oscillator chordwise locations near the leading edge and compared to traditional vortex-generating jets. While further aft-positioned oscillators produced a larger increase in maximum lift, more forward locations resulted in better poststall performance and delayed flow separation over the wing.

Passive control of 3D adaptive shock control bumps using a sealed cavity

This paper presents a Fluid–Structure-Interaction study of a novel passive adaptive shock control bump concept. A flexible plate, clamped on all sides and placed above a sealed cavity, was tested beneath a Mach 1.4 normal shock in the Imperial College London supersonic wind tunnel. The plate was actuated into the shape of a 3D shock control bump by passively controlling the cavity pressure through an array of breather holes. Preliminary experiments were performed with active control of cavity pressure (via a vacuum tank) at Mach 1.4 and 2 to illustrate the potential of this concept. Full-field surface measurement techniques, namely photogrammetry and pressure sensitive paint, were employed in addition to static pressure tappings and schlieren photography. Results confirmed that cavity pressure plays a key role in determining the aerostructural behaviour of the flexible plate. In addition, it was found that carefully placed breather holes allowed the plate to deform into a 3D shock control bump when a shock was on the flexible region and remain flat otherwise. This shows significant potential for improving the off-design behaviour of adaptive shock control bumps.

Characterization and Development of Universal Ventricular Assist Device: Computational Fluid Dynamics Analysis of Advanced Design.

We are developing a universal, advanced ventricular assist device (AVAD) with automatic pressure regulation suitable for both left and right ventricular support. The primary goal of this computational fluid dynamics (CFD) study was to analyze the biventricular performance of the AVAD across its wide range of operating conditions. An AVAD CFD model was created and validated using in vitro hydraulic performance measurements taken over conditions spanning both left ventricular assist device (LVAD) and right ventricular assist device (RVAD) operation. Static pressure taps, placed throughout the pump, were used to validate the CFD results. The CFD model was then used to assess the change in hydraulic performance with varying rotor axial positions and identify potential design improvements. The hydraulic performance was simulated and measured at rotor speeds from 2,300 to 3,600 revolutions/min and flow rates from 2.0 to 8.0 L/min. The CFD-predicted hydraulic pressure rise agreed well with the in vitro measured data, within 6.5% at 2300 rpm and within 3.5% for the higher rotor speeds. The CFD successfully predicted wall static pressures, matching experimental values within 7%. High degree of similarity and circumferential uniformity in the pump's flow fields were observed over the pump operation as an LVAD and an RVAD. A secondary impeller axial clearance reduction resulted in a 10% decrease in peak flow residence time and lower static pressures on the secondary impeller. These lower static pressures suggest a reduction in the upwards rotor forces from the secondary impeller and a desired increase in the pressure sensitivity of the pump. The CFD analyses supported the feasibility of the proposed AVAD's use as an LVAD or an RVAD, over a wide range of operating conditions. The CFD results demonstrated the operability of the pump in providing the desired circumferential flow similarity over the intended range of flow/speed conditions and the intended functionality of the AVAD's automated pressure regulation.

DEVELOPMENT OF A LIFETIME PRESSURE SENSITIVE PAINT PROCEDURE FOR HIGH-PRESSURE VANE TESTING

Abstract Optical measurements based on fast response Pressure Sensitive Paint (PSP) provide enhanced spatial resolution of the pressure field. This paper presents lifetime PSP at 20 kHz, with precise calibrations, and results from a demonstration in an annular vane cascade. The laser lifetime PSP methodology is first evaluated in a linear wind tunnel with a converging-diverging nozzle followed by a wavy surface. This test section is fully optically accessible with maximum modularity. A data reduction procedure is proposed for the PSP calibration, and optimal pixel binning is selected to reduce the uncertainty. In the annular test section, laser lifetime PSP was used to measure the time-averaged static pressure field on a section of the suction surface of a high-pressure turbine vane. Tests were performed at engine representative conditions in the Purdue Big Rig for Annular Stationary Turbine Analysis module at the Purdue Experimental Turbine Aerothermal Lab. The 2-D pressure results showed a gradual increase of pressure across the spanwise and flow directions, corroborated with local static pressure taps and computational results. The variation in PSP thickness was measured as a contribution to the uncertainty. The discrete Fourier transform of the unsteady pressure signal showed increased frequency content in wind-on compared to wind-off conditions at the mid-span and 30% span. Compared to the mid-span, the hub end wall region had an increase in frequencies and pressure amplitude. This result was anticipated given the expected presence of secondary flow structures at the near hub region.

Reconstructing Compressor Nonuniform Circumferential Flow Field From Spatially Undersampled Data—Part 2: Practical Application for Experiments

Abstract In the previous part of the paper, a novel method to reconstruct the compressor nonuniform circumferential flow field using spatially undersampled data points is developed. In this part of the paper, the method is applied to two compressor research articles to further demonstrate the potential of the novel method in resolving the important flow features associated with these circumferential nonuniformities. In the first experiment, the static pressure field at the leading edge of a vaned diffuser in a high-speed centrifugal compressor is reconstructed using pressure readings from nine static pressure taps placed on the hub of the diffuser. The magnitude and phase information for the first three dominant wavelets are characterized. Additionally, the method shows significant advantages over the traditional averaging methods for calculating repeatable mean values of the static pressure. While using the multi-wavelet approximation method, the errors in the mean static pressure with one dropout measurement are 70% less than the pitchwise-averaging method. In the second experiment, the full annulus total pressure field downstream of Stator 2 in a three-stage axial compressor is reconstructed from a small segment of data representing 20% coverage of the annulus. Results show very good agreement between the reconstructed total pressure profile and the experiment at a variety of spanwise locations from near hub to near shroud. The features associated with blade row interactions accounting for passage-to-passage variations are resolved in the reconstructed total pressure profile.

An original Pitot-static probe design for subsonic boundary layer investigation

This work presents a Pitot-static probe designed and developed to help in some boundary layer (BL) measurements, as for instance when average velocity profiles are required around models already available for wind tunnel tests but not provided with static pressure taps. The probe reads both total and static pressures at the desired location and by traversing it through the BL leads to the desired velocity measurements on the body under test, without having to rebuild the model and without using more expensive and complicated techniques. The probe is presented by describing its geometry in detail and completing the information by the relevant operating instructions. The probe response is then characterized by reporting its directional sensitivity and a validation for a standard test case. The specific probe presented here is suitable for a certain range of BL thicknesses, however the design can be easily scaled to different ranges.

Experimental steam turbine T10MW cold end cooling by water spraying

The paper deals with steam flow in experimental turbine T10MW, located in Škoda laboratory. The flow was examined for low or negative outputs of the turbine, i.e. for the so called last stages ventilation. The flow path of the turbine was in the Boiler Feed Pump Turbine (BFPT) version. It had all together 4 stages out of which two were last stages with the outlet to the condenser. In the area of each of the two outlets cooling nozzles were located with water for cooling the outlet steam flow and the area of last blades root cross-sections. Cooling of these areas is necessary due to the compression heat that occurs in the off design (ventilation) regimes. Various proportional amounts of cooling water and flowing steam were tested experimentally in constant pressure behind both last stages. Due to the fact that the flow path and the exhaust hood were fitted with many static pressure taps, thermometers and with the possibility of probing the temperature field along the outlet cross-section height, a number of results were achieved. These were mainly the turbine outputs, steam flows through the blades and cooling nozzles, determination of saturation limits in individual places at the outlet as well as temperature differences measured by the probe and stable thermometers. It was found out that the amount of cooling water was oversized for blade roots cooling, while the flow at the tip was cooled only minimally. The results are beneficial both in terms of further research of steam turbines in low regimes because this is how most newly produced machines are operated and for the designers of these machines.

CFD modelling of physical velocity and anisotropic resistance components in a peaked stored grain with aeration ducting systems

Modelling airflow in large stored grain silos has been dealt with superficial velocities and with uniform airflow resistance across the bulk. However, superficial velocities are always lower than physical velocities in an isotropic medium. Besides, due to varying grain properties, there is a high potential of variation in airflow resistances along the vertical and horizontal directions.Thus, a 3D CFD model was developed considering physical velocity in an anisotropic porous media to predict airflow and static pressure distribution from a V-shaped aeration floor. Varying airflow resistances along the horizontal direction of an element were incorporated into the model to account for the variation in grain properties. Mesh independency tests were conducted for achieving numerical stability during the steady-state simulation. The model was validated using the static pressure taps and airflow data measured in an on-farm grain storage silo.A 0.35 m mesh size was optimized using the static pressure and airflow data in the silo model. Least error for static pressure and airflow predictions were observed when horizontal airflow resistance was 50% of the vertical airflow resistance. Furthermore, the model predicted that 14.3% of the total grain volume exhibited a low airflow rate below the recommended value of 2 L s−1 t−1 including a significant proportion of the top grain volume above the eave height. Due to 85% of the non-perforated section on the silo floor, 12.6% of the lower grain volume up to a maximum height of 4.4 m above the floor exhibited the low airflow regime. As physical experimentations are tedious, the proposed physical velocity based model could be extended for simulating different options for minimizing dead zone proportions for better grain storage management.

Analysis of the Honeywell Uncertified Research Engine With Ice Crystal Cloud Ingestion at Simulated Altitudes

Abstract The Honeywell Uncertified Research Engine (HURE), a research version of a turbofan engine that never entered production, was tested in the NASA Propulsion Systems Laboratory (PSL), an altitude test facility at the NASA Glenn Research Center. The PSL is a facility that is equipped with water spray bars capable of producing an ice cloud consisting of ice particles, having a controlled particle diameter and concentration in the airflow. To develop the test matrix of the HURE, the numerical asw analysis of flow and ice particle thermodynamics was performed on the compression system of the turbofan engine to predict operating conditions that could potentially result in a risk of ice accretion due to ice crystal ingestion. The goal of the test matrix was to provide operating conditions such that ice would accrete either in the fan-stator through the inlet guide vane region of the compression system or within the first stator of the high-pressure compressor. The predictive analyses were performed with the mean-line compressor flow modeling code (comdes-melt) which includes an ice particle model. The HURE engine was tested in PSL with the ice cloud over the range of operating conditions of altitude, ambient temperature, simulated flight Mach number, and fan speed with guidance from the analytical predictions. The engine was fitted with video cameras at strategic locations within the engine compression system flow path where ice was predicted to accrete in order to visually confirm ice accretion when it occurred. In addition, traditional compressor instrumentation, such as total pressure and temperature probes, static pressure taps, and metal temperature thermocouples, were installed in targeted areas where the risk of ice accretion was expected. The current research focuses on the analysis of the data that were obtained after testing the HURE engine in PSL with ice crystal ingestion. The computational method (comdes-melt) was enhanced by computing key parameters through the fan-stator at multiple spanwise locations in order to increase the fidelity with the current mean-line method. The Icing Wedge static wet-bulb temperature thresholds were applied for determining the risk of ice accretion in the fan-stator, which is thought to be an adiabatic region. At some operating conditions near the splitter–lip region, other sources of heat (non-adiabatic walls) were suspected to be the cause of accretion, and the Icing Wedge was not applied to predict accretion at that location. A simple order-of-magnitude heat transfer model was implemented into the comdes-melt code to estimate the wall temperature minimum and maximum thresholds that support ice accretion, as observed by video confirmation. The results from this model spanned the range of wall temperatures measured on a previous engine that experienced ice accretion at certain operating conditions. The goal of this study is to show that the computational process developed on earlier engine icing tests can be used to provide an icing risk assessment in adiabatic regions for other engines.

Turbulent flow interaction with a circular cylinder

This paper presents a comprehensive experimental study on the unsteady pressure exerted on the surface of a round cylinder in smooth and turbulent flows. A highly instrumented cylinder with several static pressure taps and dynamic pressure transducers at different spanwise and peripheral locations was used, enabling extensive dynamic surface pressure, coherence, and turbulence length-scale analysis. The effects of the free-stream turbulence and turbulent length scale are investigated by placing the turbulent-generating grids within the wind tunnel duct. For both the laminar and turbulent incident flows, the surface pressure results show the emergence of the fundamental, first and second harmonics at most peripheral angles, while at the cylinder base, the surface pressure spectra are dominated by the first harmonic. It has also been observed that an increase in the level of the turbulence intensity results in an increase in the energy level of unsteady pressure acting on the cylinder. An increase in the length scale of the incoming flow structures is shown to result in an increase in the energy level of the tonal frequencies and the broadband content of the surface pressure spectra. The spanwise coherence results have also shown that an increase in the length scale of the flow structures increases the spanwise correlation length of the flow structures at the vortex shedding frequency at the stagnation point, while at the cylinder base, the spanwise correlation length decreases at the vortex shedding frequency.

EXPERIMENTAL AND NUMERICAL RESEARCH ON FLOW IN THE LAST STAGE OF 1090MW STEAM TURBINE

The paper deals with experimental and numerical research in the last stage of real 1090MW steam turbine with the last steel blade length 1220mm placed in nuclear power station. The last stage was equipped with twelve static pressure taps. It was also possible to probe in two planes - before and behind the last stage using pneumatic or optical probes. A number of last stage flow parameters were determined at the root and tip wall for nominal turbine output. Among those parameters are static pressures, Mach and Reynolds numbers, last stage reactions and steam wetness. All the directly measured and evaluated flow parameters are taken from locally measured points and that is why even 3D CFD calculation of the whole system - last stage, diffuser and exhaust hood was implemented. Measured and calculated parameters are compared. Especially static pressures are in very good agreement; the only steam wetness has bigger difference due to different measurement position. Locally measured values are enough to estimate the flow behavior of the last stage. On the other hand, the CFD simulations with well determined boundary conditions, meshes and geometry and is effective tool to simulate even very complicated flow structures in the last stage and exhaust hood.

Improvement of aerodynamic performance of a low speed axial compressor rotor blade row through air injection

This paper reveals that air injection at tip region of an axial compressor rotor blade row is an effective technique for enhancing its aerodynamic performance. Method of investigation is based on solution of the Navier–Stokes equations exploiting shear stress transport (SST) k–ω turbulence model. This model attempts to predict the turbulence by two partial differential equations for two variables of turbulence kinetic energy (k) and specific rate of dissipation (ω). Initially, computational performance curves of the proposed rotor blade row for no-injection case are compared with available experimental data, which show reasonable agreement. Then, effects of air tip injection on flow field and general aerodynamic performance of the rotor blade row are studied in detail. Results are presented in terms of the blade row span-wise distributions of total pressure rise coefficient and diffusion factor for no-injection and injection cases. Flow patterns at the blade row tip region are also carefully demonstrated. Six pseudo static pressure taps were mounted along the blade chord line within the blade tip gap region for detection of the flow fluctuations. So, it was possible to extract frequency spectrum of the fluctuating flow in this region. Numerical simulations confirmed that injection of air flow at the blade row tip region boosts the flow momentum and reduces blockages due to the flow separation from the blades surfaces. Results showed that air injection as small as of only 0.5% of the whole annulus mass flow rate causes the stall margin of the rotor blade row to increase by 15.5%.

Flowfield and Performance Analysis of a Three-Dimensional TBCC Exhaust Nozzle

Compared to other engines, turbine-based combined cycle (TBCC) engine is one of the most suitable propulsion systems for hypersonic vehicle. Because of its fine reusability, wide flight envelope, and safety margins, TBCC engine is becoming a more and more important hotspot of research. In this paper, a three-dimensional (3D) over–under TBCC exhaust system is designed, simulated, and the results are discussed, wherein the ramjet flowpath is designed by the quasi-two-dimensional method of characteristics (MOC). A new scheme of rotating around the rear shaft is proposed to regulate the throat area of turbine flowpath. Cold flow experiments are conducted to gain a thorough and fundamental understanding of TBCC exhaust system at on and off-design conditions. To characterize the flow regimes, static pressure taps and schlieren apparatus are employed to obtain the wall pressure distributions and flowfield structures during the experiments. Detailed flow features, as well as the thrust performance, are simulated by the computational fluid dynamics (CFD) method. Both the numerical and experimental results show that the TBCC exhaust nozzle in this study can provide sufficient thrust during the whole flight envelop despite a little deterioration at the beginning of the mode transition. The research provides a new and effective scheme for the exhaust system of TBCC engine.

Study on Hydraulic Performances of a 3-Bladed Inducer Based on Different Numerical and Experimental Methods

The hydraulic performances of a 3-bladed inducer, designed at Alta, Pisa, Italy, are investigated both experimentally and numerically. The 3D numerical model developed in ANSYS CFX to simulate the flow through the inducer and different lengths of its inlet/outlet ducts is illustrated. The influence of the inlet/outlet boundary conditions, of the turbulence models, and of the location of inlet/outlet different pressure taps on the evaluation of the hydraulic performance of the inducer is analyzed. As expected, the predicted hydraulic performance of the inducer is significantly affected by the lengths of the inlet/outlet duct portions included in the computations, as well as by the turbulent flow model and the locations of the inlet/outlet pressure taps. It is slightly affected by the computational boundary conditions and better agreement with the test data obtained when adopting the k-ω turbulence model. From the point of the pressure tap locations, the pressure rise coefficient is much higher when the inlet/outlet static pressure taps were chosen in the same locations used in the experiments.

Estimation of the correction term of pitot tube measurements in unsteady (gusty) flows

In rough environments (train’s underbody, wind carrying sand etc.), the only feasible means of measuring flow speed is with a Pitot tube. Unsteady (gusty) flow effects can cause large errors in flow speed measurements. In this short communication work, an attempt has been made to identify these errors. Based on potential flow theory, a term that takes into account the unsteady effects has been proposed to correct the Pitot tube measurements in unsteady (gusty) flow conditions. Experiments have been performed in an open circuit-closed test-section, low-speed wind tunnel, designed and built at the Instituto de Microgravedad “Ignacio Da Riva” of the Universidad Politécnica de Madrid (IDR/UPM). Different types of Pitot tubes have been used to check the validity of the correction term proposed. It has been shown that the distance between the total and static pressure taps has a major influence on the Pitot tube correction term.

The role of free stream turbulence with large integral scale on the aerodynamic performance of an experimental low Reynolds number S809 wind turbine blade

Effects of free stream turbulence with large integral scale on the aerodynamic performance of an S809 airfoil-based wind turbine blade at low Reynolds number are studied using wind tunnel experiments. The case of wind turbine blades subjected to turbulence structures with large integral scale is of interest since in the atmospheric boundary layer very large-scale structures interact with the blades. A constant chord (2-D) S809 airfoil wind turbine blade model with an operating Reynolds number of 2.08×105 based on chord length was tested for a range of angles of attack representative of fully attached and stalled flow as encountered in typical wind turbine operation. The smooth-surface blade was subjected to a quasi-laminar free stream with very low free-stream turbulence as well as to elevated free-stream turbulence generated by an active grid. This turbulence contained large-scale eddies with levels of free-stream turbulence intensity of up to 6.14% and an integral length scale of about 60% of chord-length. The pressure distribution was acquired using static pressure taps and the lift was subsequently computed by numerical integration. The wake velocity deficit was measured utilizing hot-wire anemometry to compute the drag coefficient also via integration. In addition, the mean flow was quantified using 2-D particle image velocimetry (PIV) over the suction surface of the blade. Results indicate that turbulence, even with very large-scale eddies comparable in size to the chord-length, significantly improves the aerodynamic performance of the blade by increasing the lift coefficient and overall lift-to-drag ratio, L/D for all angles tested except 0°.

Numerical Study of Wall Ventilation in a Transonic Wind Tunnel

Transonic wind tunnels (TWT) are sophisticated tools for the investigations of flows with Mach numbers of order one. The most characteristic feature of a facility such as this is, for sure, the openings in the walls of the test section. The openings in the walls permit the proper relief effect, and this, on the other hand, makes possible the experimentation at the transonic range. The results to be presented in this paper correspond to an analysis of the flow in the test section of a TWT containing a NACA 0012 airfoil. Both numerical and experimental investigations were conducted. For the numerical investigation, a threedimensional, finite-difference code, based on the diagonalalgorithm, was employed, whereas for the experimentation, the classical static-pressure taps as well as the pressure sensitive paint (PSP) techniques were used. The classical static-pressure tap method is indicated as PSI technique. The pressure distributions were investigated for Mach numbers in the range of 0.6 – 0.8 and angles of attack from 0° up to 8°. The relief effect due to the slots, which provides for avoiding choking effects, is clearly demonstrated when one compares the flow along both solid and perforated walls. In the first part of this research report, the main focus will be on the numerical results. Notwithstanding this, and for comparison purposes, some experimental results will be called upon here, together with some literature data.