Nondimensional Rotational Speed Research Articles

On the transitional wake past a streamwise rotating prolate spheroid

Direct numerical simulations are performed to study the behavior of the wake behind a 5:2 streamwise rotating prolate spheroid. The Reynolds number Re = 1000 under different rotational speeds over a large range of 0≤Ω≤3 is considered, where Ω is the non-dimensional rotational speed based on the freestream velocity and the volume-equivalent diameter of the prolate spheroid. By successively increasing the rotational speed, seven distinct flow regimes were identified and explored: steady state, low-speed steady rotation state, axisymmetric state, high-speed steady rotation state, twofold rotational symmetrical state (TFRS), quasi-periodic vortex shedding state (QVS), and weakly chaotic state. Among these wake regimes, the TFRS regime is reported for the first time, and it can be interpreted as an outcome of the stabilizing influence of the spheroid's rotation acting to restore the wake structure to an axisymmetric state. It is found that the rotation of the prolate spheroid has a stabilizing effect under low rotational speeds. Furthermore, the coupling mechanism between the rotational double helical structure and vortex shedding in the QVS regime has been revealed. The results of this study contribute to closing the knowledge gap regarding the wake dynamics of a streamwise rotating prolate spheroid.

Cooling performance improvement for two hot elastic plates by using double channels with rotating cylinders

Abstract Alternative cooling systems that can be used for thermal management in different technological applications such as in batteries, solar panels, electronic systems and in diverse heat transfer equipments are needed. This study uses a hybrid channel system with rotating circular cylinders to explore the cooling of two heated elastic plates. The numerical analysis of a coupled fluid-structure-thermal system with rotating cylinders is done using the finite element technique with ALE. The study is carried out for different values of the Reynolds number (Re) in the upper channel flow (between 200 and 1000), the non-dimensional rotational speeds of the cylinders (Ω in the range between -1000 and 1000), and the non-dimensional location of the cylinders (between 0.4 and 1) taking into account the cooling of both the rigid and elastic plates. Rigid plates have better cooling performance than elastic ones. The cooling performance increases for both rigid and elastic plates reach up to 26.1% and 31.7% at the maximum upper channel flow Re. For elastic and rigid plates, CCW rotation at maximum speed increases cooling performance by 18.5% and 19%, respectively, but CW rotation increments cooling performance by only 7%. By using optimization, the cooling performance increase with rotatingcylinders at Re=200 is determined to be 73.6% more than that of the case without cylinders. Optimization results in an extra 11.2% increase in cooling performance at Re=1000 when compared to the parametric CFD scenario

Wall effect on the wake characteristics of a transversely rotating sphere

In the present work, the flow over a transversely rotating sphere placed at varying separation from a plane wall at a Reynolds number Re=U∞Dν of 300 is numerically investigated using Open Source Field Operation and Manipulation, where Re is defined based on the free stream velocity (U∞) and the diameter (D) of the sphere. Three values of the non-dimensional rotational speed ω*=ωD2U∞, viz., −1, 0 and 1, have been chosen with ω being the dimensional rotation rate with anticlockwise rotation being positive. The non-dimensional separation gap G=gD between the sphere and the wall is varied from 0.25 to 3.0. Here, g is the dimensional gap between the sphere and the wall. At ω*=0 and G = 0.25, the wall completely suppresses vortex shedding from the sphere, whereas flow is found to be unsteady for other values of ω* and G. As compared to the case in the absence of the wall, the presence of the wall causes an increase in vortex shedding frequency for ω*=0 and 1 and decrease for ω*=−1. Hilbert spectrum reveals that the wake nonlinearity remains unchanged with an increase in G for ω*=0. On the other hand, it increases for ω*=−1 and decreases for ω*=1. Similar to the observation made for vortex shedding, the presence of wall increases drag force on the sphere for ω*=0 and 1 and decreases for ω*=−1. In order to reveal the spatial and temporal behavior of the coherent structures in the unsteady wake, dynamic mode decomposition (DMD) has been performed. For all the values of G, DMD mode 1 is found to be the primary vortex shedding mode.

Nonlocal wave propagation analysis of a rotating nanobeam on a Pasternak foundation

In this paper, the wave propagation analysis of a cantilever rotating nanobeam modeled as a thin beam based on the Euler–Bernoulli theory on a Pasternak foundation has been investigated using the nonlocal theory of elasticity. The governing partial differential equation of motion for a uniform rotating nanobeam is derived using the Hamilton principle considering the nonlocal parameter of small scale effect. The Spectrum and dispersion relations of non-dimensional wave number are obtained analytically. The effect of changes of different parameters including nonlocal scale parameter, non-dimensional rotational speed, non-dimensional rotational wave frequency ratio, and shear stiffness of the Pasternak foundation on the wave dispersion behavior of the non-dimensional wave number and phase and group speeds dispersions for the rotating nanotube have been studied. It is observed that the wave dispersion characteristics of the rotating nanobeam are extremely influenced by rotational speed, wave number, nonlocal length scale parameter, and shear stiffness of the Pasternak foundation. Moreover, the propagated flexural wave has been shown to exhibit non-dispersive behavior at very high rotational speeds.

Control of Magnetohydrodynamic Mixed Convection and Entropy Generation in a Porous Cavity by Using Double Rotating Cylinders and Curved Partition.

In this work, mixed convection and entropy generation analyses in a partitioned porous cavity with double inner rotating cylinders are explored under magnetic field effects. A curved partition shape is considered with identical rotating cylinders and an inclined magnetic field, while the right vertical wall moves with a constant speed in the y-direction. Numerical simulations are performed by considering various values of Rayleigh number, Hartman number, Darcy number, inclination of the magnetic field, size of the curved partitions, and rotational speeds of the inner cylinders and their vertical locations with the cavity. Complicated flow field with multicellular structures are observed due to the complex interaction between the natural convection, moving wall, and rotational effects of inner cylinders. Improved heat-transfer performance is obtained with higher values of magnetic field inclination, higher values of permeability/porosity of the medium, and higher rotational speeds of the cylinders. Almost doubling of the average Nu number is obtained by decreasing the value of the Hartmann number from 25 to 0 or varying the magnetic field inclination from 90 to 0. When rotational effects of the cylinders are considered, average heat-transfer improvements by a factor of 5 and 5.9 are obtained for nondimensional rotational speeds of 5 and −5 in comparison with the case of motionless cylinders. An optimum length of the porous layer is achieved for which the best heat-transfer performance is achieved. As the curvature size of the partition is increased, better heat transfer of the hot wall is obtained and up to 138% enhancement is achieved. Significant increments of entropy generation are observed for left and right domains including the rotating cylinders. The magnetic field parameter also affects the entropy generation and contributions of different domains including the curved porous partition.

Flow and heat transfer across two inline rotating cylinders: Effects of blockage, gap spacing, Reynolds number, and rotation direction

The manipulation of the heat transfer and flow field using cylinder rotation is of a classical issue. It is of fundamental importance to study the dependence of wake and thermal topologies of two rotating cylinders in tandem arrangements. This study numerically investigates the time-resolved laminar flow, fluid forces, Strouhal number, and convective heat transfer over two isothermal co-rotating and counter-rotating circular cylinders in tandem arrangements for scaled cylinder center-to-center spacing S* = 2.5 - 6, non-dimensional rotational speed |α| ≤ 5, and Reynolds number Re = 100 - 200. How Re, S*, α and computational domain size influence the wake dynamics and thermal attributes is the focus of this study. The numerical procedure is validated against the available data in the literature for a single rotating cylinder. The influence of the blockage ratio on the single- and two-cylinder flow is determined first to decide the appropriate computational domain. It is found that rotating cylinders require a larger computational domain (blockage ratio ≈ 1%, when α> 2) than stationary cylinders (blockage ratio = 5%). The fluid forces are highly sensitive to the cylinder rotation when |α| > 2. Although both cylinders undergo the same magnitudes of time-mean drag coefficient |C¯d| or time-mean lift coefficient |C¯l| at a given |α|, the cylinder rotation shifting from co-rotation to counter-rotation reverses the direction of C¯d, i.e. repulsive for the co-rotation and attractive for the counter-rotation. On the other hand, an increase in S* from 2.5 to 6 with α = 5 results in a 43% drag reduction for either cylinder. The S*, however, has an insignificant effect on C¯l (e.g. upto 5.3% at α = 5) while Re increases both vortex shedding frequency (e.g. 16.8% at α = 1) and heat transfer (e.g. upto 73.3% at α = 1). A flow map in a three-dimensional domain of S*, α and Re is provided, distinguishing steady and unsteady flows. Four distinct flow regimes are labeled, namely steady flow, alternate coshedding (AC) flow, single rotating bluff-body (SRB) flow, and inverted-rotation (IR) flow. An increase in |α| causes a modification of the AC flow to a steady flow and then to a SRB or IR flow.

Wake of transversely rotating and translating sphere in quiescent water at low Reynolds number

The unsteady wake of a rotating and translating sphere is experimentally investigated at Reynolds numbers (Re) ranging from 115 to 550 for two rotational speeds. Non-dimensional rotational speed, $$\Omega^{ * }$$ , is defined as the ratio of the maximum azimuthal speed of the sphere and the speed of translation. Motion of the sphere is generated using a specially designed mechanism in a channel, and its wake has been visualized using fluorescent dye. Unlike the steady flow past a stationary sphere where the limiting Reynolds number is 270, the flow becomes unsteady when sufficient rotation rate is introduced at much lower Reynolds number ( $${\text{Re}} = 115,\Omega^{ * } = 0.375$$ ). The transition from one-sided to double-sided hairpin vortex occurs at one critical Re for a given rotational speed, and it switches back to one-sided hairpin vortex shedding at another critical Re. Particle image velocimetry results demonstrate the vorticity distribution in the wake and the variation of the wake width with axial distance. At very low Re, velocity profiles in the wake are nearly self-similar. The strength of the vortex rings weakens in the far wake. The decay of centerline velocity in axial direction confirms the dissipation of the vorticity in the far wake. In this unsteady flow, the time-averaged value of the separation angle is higher than that of the steady flow on the advancing side due to enhanced adverse pressure gradient. The Strouhal number calculated from the dye visualization in this range of $$\Omega^{ * }$$ and Re varies from 0.175 to 0.25, a clear increasing trend both with increasing Re and $$\Omega^{ * }$$ . The coefficient of drag evaluated at the center plane remains constant at 0.94 for the present investigation up to $${\text{Re}} = 550$$ . The wavelength of the unstable hairpin vortices is found to scale inversely with the translational velocity of the sphere.

Unsteady forced convection heat transfer of a stationary and rotating sphere: Experimental Investigation

Unsteady forced convection heat transfer of a stationary and rotating sphere in an open-loop air system was experimentally investigated with an aim to evaluate the influence of sphere rotation rate on the heat transfer enhancement. A special-purpose conical diffuser having a circular cross-section with constant divergence angle has been carefully designed and adopted as a passive rotating technique. The effect of inlet Re number, non-dimensional rotational speed, and initial surface temperature on heat transfer enhancement are examined. It is observed from the comparison made that there are significant differences between the stationary and rotating sphere of heat transfer behavior. The experimental results of heat transfer behavior in terms of heat flux q and Nusselt number Nu, respectively, expose that q decreases with increase of non-dimensional rotational speed, while Nu increases with the increase of non-dimensional rotational speed around 600%.

Characterisation of turbine behaviour for an engine overspeed prediction model

This paper focuses on the characterisation of turbine overspeed behaviour to be integrated into an engine overspeed model capable of predicting the terminal speed of the high pressure turbine (HPT) in the event of a high pressure shaft failure. The engine considered in this study features a single stage HPT with a shrouded contra-rotating rotor with respect to the single stage intermediate pressure turbine (IPT). The HPT performance is characterised in terms of torque and mass flow function for a range of expansion ratios at various non-dimensional rotational speeds (NH), up to 200% of the design value. Additionally, for each HPT expansion ratio and NH, the change in capacity of the downstream IPT, for different IPT non-dimensional rotational speeds (NI), also needs to be characterised due to the extremely positive incidence angle of the flow from the upstream rotor. An automated toolkit is developed to generate these characteristic maps for both the HPT and IPT.An unlocated high pressure shaft failure will result in rearward movement of the rotor sub-assembly. This causes changes in the rotor tip and rim seal regions, and in the rim seal leakage flow properties. Therefore, in the present work, a high fidelity characterisation of turbine behaviour with the inclusion of tip and rim seals is carried out at three different displacement locations, 0 mm, 10 mm and 15 mm, to improve terminal speed estimation. Furthermore, there is a possibility of damage to the tip seal fins of the HPT rotor due to unbalance in the spool that may result in contact between the rotor aerofoil tip and the casing. Consequently, another set of characteristics are generated with damaged tip fins at each displacement location.It is observed from the characteristics that the torque of the HPT rotor decreases with increasing NH. The HPT mass flow function initially decreases and then increases with an increase in NH. The IPT mass flow function initially remains similar and then decreases with increase in NH above values of 150%. The HPT rotor torque and IPT mass flow function decrease with rearward movement of the HPT rotor sub-assembly for all values of NH. With worn tip seal fins all parameters mentioned previously are lower than in the nominal undamaged case. The high fidelity characterisation of turbines that follows the sequence of events after a shaft failure, as described in this work, can provide accurate predictions of terminal speed and thus act as a tool for testing design modifications that can result in better management and control of the over-speed event.

Free vibration analysis of a rotating non-uniform functionally graded beam

In this paper, free vibration characteristics of a rotating double tapered functionally graded beam is investigated. Material properties of the beam vary continuously through thickness direction according to the power-law distribution of the volume fraction of the constituents. The governing differential equations of motion are derived using the Hamilton's principle and solved utilizing an efficient and semi-analytical technique called the Differential Transform Method (DTM). Several important aspects such as taper ratios, rotational speed, hub radius, as well as the material volume fraction index which have impacts on natural frequencies of such beams are investigated and discussed in detail. Numerical results are tabulated in several tables and figures. In order to demonstrate the validity and accuracy of the current analysis, some of present results are compared with previous results in the literature and an excellent agreement is observed. It is showed that the natural frequencies of an FG rotating double tapered beam can be obtained with high accuracy by using DTM. It is also observed that nondimensional rotational speed, height taper ratio, power-law exponent significantly affect the natural frequencies of the FG double tapered beam while the effects of hub radius and breadth taper ratio are negligible.

Electrothermal effects of advanced electromagnetic materials on electrical loss and thermal characteristics of synchronous rotational machines

Electrothermal characteristics of high speed synchronous rotational machine were studied experimentally and theoretically. Electrical rotating machines with three types of electromagnetic materials were fabricated to identify core losses in the iron cores of high speed synchronous machine. Dummy and isolated rotational machines were devised to measure pure mechanical losses and to examine conductive thermal resistances in stators. Results showed that mechanical losses are linearly proportional to driving speeds of electrical rotating machines, and that viscosity-induced mechanical losses in air are relatively negligible in comparison with friction-induced mechanical losses. It was found that an electrical rotating machine with 15HTH1000 electromagnetic material has relatively lower core and coil losses than the machines with 35PN440, 35PN250, thereby making it applicable for advanced high speed electric vehicular applications. In addition, core materials had a negligible effect on torque constants of the electrical rotating machines at a lower non-dimensional rotational speed of 0.2. However, the rotating machine with 15HTH1000 showed an 8.0% higher input current than did that with 35PN440 at a higher rotational speed of 0.9. Finally, thermal resistances in between iron cores and stators could be accurately characterized by a nonlinear empirical formula with the minimum R2 value of curve fittings equal to 0.997 which reflects the convection effects on heat transfer enhancement.

Numerical simulations of flow fields through conventionally controlled wind turbines & wind farms

In the current study, an Actuator-Line Model (ALM) is implemented in our in-house pseudo-spectral LES solver SP-WIND, including a turbine controller. Below rated wind speed, turbines are controlled by a standard-torque-controller aiming at maximum power extraction from the wind. Above rated wind speed, the extracted power is limited by a blade pitch controller which is based on a proportional-integral type control algorithm. This model is used to perform a series of single turbine and wind farm simulations using the NREL 5MW turbine. First of all, we focus on below-rated wind speed, and investigate the effect of the farm layout on the controller calibration curves. These calibration curves are expressed in terms of nondimensional torque and rotational speed, using the mean turbine-disk velocity as reference. We show that this normalization leads to calibration curves that are independent of wind speed, but the calibration curves do depend on the farm layout, in particular for tightly spaced farms. Compared to turbines in a lone-standing set-up, turbines in a farm experience a different wind distribution over the rotor due to the farm boundary-layer interaction. We demonstrate this for fully developed wind-farm boundary layers with aligned turbine arrangements at different spacings (5D, 7D, 9D). Further we also compare calibration curves obtained from full farm simulations with calibration curves that can be obtained at a much lower cost using a minimal flow unit.

On the dynamics of rotating, tapered, visco-elastic beams with a heavy tip mass

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.

Preliminary Design and Performance Estimation of Radial Inflow Turbines: An Automated Approach

A comprehensive one-dimensional meanline design approach for radial inflow turbines is described in the present work. An original code was developed in Python that takes a novel approach to the automatic selection of feasible machines based on pre-defined performance or geometry characteristics for a given application. It comprises a brute-force search algorithm that traverses the entire search space based on key non-dimensional parameters and rotational speed. In this study, an in-depth analysis and subsequent implementation of relevant loss models as well as selection criteria for radial inflow turbines is addressed. Comparison with previously published designs, as well as other available codes, showed good agreement. Sample (real and theoretical) test cases were trialed and results showed good agreement when compared to other available codes. The presented approach was found to be valid and the model was found to be a useful tool with regards to the preliminary design and performance estimation of radial inflow turbines, enabling its integration with other thermodynamic cycle analysis and three-dimensional blade design codes.

The influences of both offset and mass moment of inertia of a tip mass on the dynamics of a centrifugally stiffened visco-elastic beam

The present study is concerned with the out-of-plane vibrations of a rotating, internally damped (Kelvin-Voigt model) Bernoulli-Euler beam carrying a tip mass. The centroid of the tip mass, possessing also a mass moment of inertia is offset from the free end of the beam and is located along its extended axis. This system can be thought of as an extremely simplified model of a helicopter rotor blade or a blade of an auto-cooling fan. The differential eigenvalue problem is solved by using Frobenius method of solution in power series. The characteristic equation is then solved numerically. The simulation results are tabulated for a variety of the nondimensional rotational speeds, tip mass, tip mass offset, mass moment of inertia and internal damping parameters. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained. Some numerical results are given in graphical form. The numerical results obtained, indicate clearly that the tip mass offset and mass moment of inertia are important parameters on the eigencharacteristics of rotating beams so that they have to be included in the modeling process.

A numerical study of convective heat transfer from a rotating cylinder with cross-flow oscillation

This article presents a numerical investigation of convective heat transfer from a rotating cylinder with cross-flow oscillation. A finite element analysis using Characteristic Based Split method (CBS) is developed to solve governing equations involving continuity, Navier–Stokes, and energy equations. Dynamic unstructured triangular grid is used employing improved lineal and torsional spring analogy which is coupled with the solver by the Arbitrary Lagrangian–Eulerian (ALE) formulation. After verifying the numerical code accuracy, simulations are conducted to study convective heat transfer past a rotating cylinder with cross-flow oscillation at Reynolds numbers of 50, 100, and 200. Different rotational speeds of the cylinder normalized by free stream velocity, in the range of 0–2.5 are considered at various oscillating amplitudes and frequencies and three different Prandtl numbers of 0.7, 6, and 20. Effects of oscillation and rotation of cylinder on the temperature and flow field, vortex lock-on, mean Nusselt number, and the pattern of vortex shedding are investigated in detail considering iso-temperature and iso-flux boundary conditions on the cylinder surface. It is found that similar to the fixed cylinder, beyond a critical rotating speed, vortex shedding is mainly suppressed. Also by increasing the non-dimensional rotational speed of the cylinder, both the Nusselt number and the drag coefficient decrease rapidly. However, in vortex lock-on region, the Nusselt number increases in a large amount.

A numerical investigation of fluid flow over a rotating cylinder with cross flow oscillation

This paper studies a two-dimensional incompressible viscous flow past a rotating cylinder with cross flow oscillation using a finite element method based on the characteristic based split (CBS) algorithm to solve governing equations including full Navier–Stokes and continuity equations. Dynamic unstructured triangular grid is used employing lineal and torsional spring analogy which is coupled with the solver by an Arbitrary Lagrangian–Eulerian (ALE) formulation. After verifying the accuracy of the numerical code, simulations are conducted for the flow past a rotating cylinder with cross flow oscillation at moderate Reynolds numbers of 50, 100, and 200 considering different non-dimensional rotational speeds based on the free-stream velocity in the range 0–2.5, and various oscillating amplitudes and frequencies. Effects of the oscillation and rotation of the cylinder on the vortex shedding both in lock-on and non-lock-on regions, the mean drag and lift coefficients, and the Strouhal number are investigated in detail. It is found that similar to the fixed cylinder beyond a critical non-dimensional rotational speed the vortex shedding is highly suppressed. In addition, by increasing the rotational speed of the cylinder, the lift coefficient increases while decreasing the drag coefficient. However, in the vortex lock-on region both the lift and the drag coefficients increase significantly.

On the eigencharacteristics of a centrifugally stiffened, visco-elastic beam

The present study is concerned with the out-of-plane vibrations of a rotating, internally damped (Kelvin—Voigt model) Bernoulli—Euler beam carrying a tip mass, which can be thought of as a simplified model of a helicopter rotor blade or a blade of an auto-cooling fan. The differential eigenvalue problem set up is solved by using the Frobenius method of solution in a power series. The developed characteristic equation is then solved numerically. The simulation results are tabulated for a variety of non-dimensional rotational speeds, tip mass, and internal damping parameters. These are compared with the results of conventional finite element (FE) modelling as well and excellent agreement is obtained. Furthermore, it is seen that the numerical calculations according to the proposed solution method need much less computer time as compared to the conventional FE method.

Wake structure of a transversely rotating sphere at moderate Reynolds numbers

The uniform flow past a sphere undergoing steady rotation about an axis transverse to the free stream flow was investigated numerically. The objective was to reveal the effect of sphere rotation on the characteristics of the vortical wake structure and on the forces exerted on the sphere. This was achieved by solving the time-dependent, incompressible Navier–Stokes equations, using an accurate Fourier–Chebyshev spectral collocation method. Reynolds numbers Re of 100, 250 and 300 were considered, which for a stationary sphere cover the axisymmetric steady, non-axisymmetric steady and vortex shedding regimes. The study identified wake transitions that occur over the range of non-dimensional rotational speeds Ω* = 0 to 1.00, where Ω* is the maximum velocity on the sphere surface normalized by the free stream velocity. At Re = 100, sphere rotation triggers a transition to a steady double-threaded structure. At Re = 250, the wake undergoes a transition to vortex shedding for Ω* ≥ 0.08. With an increasing rotation rate, the recirculating region is progressively reduced until a further transition to a steady double-threaded wake structure for Ω* ≥ 0.30. At Re = 300, wake shedding is suppressed for Ω* ≥ 0.50 via the same mechanism found at Re = 250. For Ω* ≥ 0.80, the wake undergoes a further transition to vortex shedding, through what appears to be a shear layer instability of the Kelvin–Helmholtz type.

The representation of GT component maps using Mach numbers

AbstractComponent maps are produced under certain environmental conditions using air as the working fluid during static ground operation. Any changes of the component characteristics when operating under different temperature conditions and/or with different working fluid are partially taken into account, because of the existence of the gas constant and the ratio of the specific heats in the non-dimensional mass flow and rotational speed. This provides a second order correction for the component characteristics, which may be adequate for the initial modeling of engines. However, for rigorous performance calculations correction factors are applied to the non-dimensional mass flow, rotational speed and pressure ratio distributions of a map, when deviations from the reference conditions under which it was extracted, are experienced. In the current study, a different approach is considered in order to eliminate the inaccuracies caused by the varying temperature and chemical composition. It makes direct use of inlet and circumferential Mach numbers based upon stagnation temperature in conjunction with dimensionless enthalpy variation. A sensitivity analysis against gas property variations is conducted to quantify the benefits gained in precision. Generally, the well-known relationships correlating the Mach number with total and static properties are based on the assumption of perfect gas and constant gas properties. Introducing dependency on temperature and/or chemical composition for the caloric properties of the semi-perfect gas, proper mean values are defined and some theoretical corrections are provided for the well-known equations. The mass flow compatibility equation is then based on the ‘corrected’ expression correlating dimensionless mass flow and Mach number and takes full account of gas property variations.