Rms Temperature Fluctuations Research Articles

Investigation of Sub-Grid Scale Turbulence-Radiation Interaction Effects on Turbulence Energy Transport and Varying Thermophysical Properties Using Large Eddy Simulation

Abstract The main objective of this article is to investigate sub-grid scale turbulence–radiation interaction (SGS TRI) effects on SGS turbulence kinetic energy (TKE) fluctuations and varying thermophysical properties in a partially premixed combustion system for a laboratory-piloted methane/air flame. The large eddy simulation approach is employed to simulate the turbulence of the compressible reactive flow. SGS quantities, including turbulent stress and fluxes of enthalpy and species in the sub-grid scale, are computed using the standard Smagorinsky–Lilly model. The radiative transfer equation is modeled by applying the spherical harmonic P1 approximation by considering the radiative heat source related to the SGS TRI contribution. Optically thin fluctuation approximation is utilized to simplify the radiative absorption term. A chemical reaction mechanism comprising 41 steps and 16 species is applied to model methane–air mixture combustion. Diffusion flamelet-generated manifolds are employed to govern the species transport equation. About 87% of TKE is resolved by applying the finest grid consisting of 1,822,580 cells. Impacts of SGS TRI on the spatially filtered density, eddy viscosity, SGS velocity and TKE, overall radiative emission, RMS temperature fluctuations, and nitrogen monoxide (NO) formation are studied. The results reveal that considering SGS TRI in the simulation leads to remarkable discrepancies, particularly in SGS velocity and TKE by 6.70% and 7.40%, respectively. Meanwhile, SGS density and eddy viscosity deviate negligibly in the presence of SGS TRI. Also, the filtered mass fraction of NO reduces up to 17.54% on average by considering TRI.

Resilience of parity-violation-induced chiral selectivity to nonequilibrium temperature fluctuations in open systems

We consider the sensitivity of chemical reactions, able to undergo spontaneous mirror symmetry breaking, to chiral bias in the presence of nonequilibrium temperature fluctuations and derive a selectivity criterion. For this, we estimate the magnitude of fluctuations $\ensuremath{\delta}k$ in chemical reaction rate constants $k$ arising from the nonequilibrium temperature fluctuations $\ensuremath{\delta}T$ about a mean value $T$. To leading order, the relative rate constant fluctuations $\ensuremath{\delta}{k}_{i}/{k}_{i}$ for each reaction $i$ are given by the product of the activation enthalpy $\mathrm{\ensuremath{\Delta}}{H}_{i}^{\ifmmode\ddagger\else\textdaggerdbl\fi{}}/RT$ for the $i\mathrm{th}$ reaction multiplied by the relative rms temperature fluctuations $\ensuremath{\delta}{T}_{\mathrm{rms}}/T$. The latter are determined by the system's specific heat at constant volume: ${C}_{V}$. We test this criterion with simulations carried out for an open-flow fully reversible Frank model, and for a range of parity-violating energy differences (PVED) within the theoretically estimated upper and lower bounds. Depending on the relative magnitudes of the deterministic PVED bias and the temperature fluctuations, the PVED bias can either (i) select the final stable chiral outcome deterministically or (ii) select one of two possible stable chiral outcomes with an asymmetric statistical weighting. For larger temperature fluctuations, the PVED bias loses its selectivity, and the final stable chiral outcomes are stochastic and equally probable. This paper points towards the possible design of small volume chemical flow reactors capable of detecting the elusive PVED bias in bulk systems, provided other sources of fluctuations can be sufficiently controlled and attenuated.

3D unsteady and steady modeling of heat and mass transfer during Cz Si crystal growth with a horizontal magnetic field

A combined LES/RANS approach is applied to modeling Czochralski (Cz) Si growth with a strong horizontal magnetic field stabilizing the melt flow. A model furnace geometry with a cylindrical crucible is considered, which can be suggested for benchmarking Cz Si melt convection of industrial scale. Grid resolution in boundary layers is carefully adjusted and the 4th approximation order for diffusion terms is shown to provide sufficient computation accuracy even with comparatively rough grids. The computed flow structure, temperature distribution on the melt free surface, and RMS temperature fluctuations of the melt are in good agreement with published experimental data and modeling results for industrial furnaces. The effect of the crystal rotation rate on the interface shape and oxygen incorporation into the crystal is analyzed. Due to high thermal conductivity (or low Pr number) of the melt, the unsteady oscillations do not exert a significant effect on the temperature and heat flux distribution in the melt, which allows quite accurate predictions of the interface shape, even neglecting the flow unsteadiness. In contrast, due to a low diffusivity (or high Sc number) of atomic oxygen in the melt, the unsteady oscillations quite significantly affect its transport through the melt and incorporation into the crystal, which results in remarkable overestimation of the oxygen concentration without consideration of unsteady melt flow evolution. The formulation of the LES/RANS approach used in the benchmark problem was verified on experimental data for an industrial furnace for Magnetic Cz (MCz) growth of 300 mm silicon crystals.

Convection with misaligned gravity and rotation: simulations and rotating mixing length theory

ABSTRACT We present numerical simulations, using two complementary set-ups, of rotating Boussinesq thermal convection in a three-dimensional Cartesian geometry with misaligned gravity and rotation vectors. This model represents a small region at a non-polar latitude in the convection zone of a star or planet. We investigate the effects of rotation on the bulk properties of convection at different latitudes, focusing on determining the relation between the heat flux and temperature gradient. We show that our results may be interpreted using rotating mixing length theory (RMLT). The simplest version of RMLT (due to Stevenson) considers the single mode that transports the most heat. This works reasonably well in explaining our results, but there is a systematic departure from these predictions (up to approximately $30{{\ \rm per\ cent}}$ in the temperature gradient) at mid-latitudes. We develop a more detailed treatment of RMLT that includes the transport afforded by multiple modes, and we show that this accounts for most of the systematic differences. We also show that convectively generated zonal flows and meridional circulations are produced in our simulations, and that their properties depend strongly on the dimensions of the box. These flows also affect the heat transport, contributing to departures from RMLT at some latitudes. However, we find the theoretical predictions of the multi-mode theory for the mid-layer temperature gradient, the root-mean-square (rms) vertical velocity, the rms temperature fluctuation, and the spatial spectrum of the heat transport at different latitudes are all in reasonably good agreement with our numerical results when zonal flows are small.

LES of supersonic minimal channel flow between isothermal walls at different temperatures including thermal radiation effects using a fictitious gray gas

Large-eddy simulation of a supersonic channel flow between isothermal walls at different temperatures is performed to study radiation effects using a fictitious gray gas model. The simulations are carried out at two different resolutions to ascertain the effects of subgrid scales on radiation. Effects of radiation on the mean temperature, on RMS temperature fluctuations as well as on the turbulence structure are presented. For the moderate optical thickness of the flow considered here, the effects of subgrid scales on the radiative heat transfer are found to be small.

Rotational Raman-based temperature measurements in a high-velocity, turbulent jet

Spontaneous rotational Raman scattering spectroscopy is used to acquire measurements of the mean and root mean square (rms) temperature fluctuations in turbulent, high-velocity heated jets. Raman spectra in air were obtained across a matrix of radial and axial locations downstream from a 50 mm diameter nozzle operating from subsonic to supersonic conditions over a wide range of temperatures and Mach numbers, in accordance with the Tanna matrix frequently used in jet noise studies. These data were acquired in the hostile, high noise (115 dB) environment of a large scale open air test facility at NASA Glenn Research Center (GRC). Temperature estimates were determined by performing non-linear least squares fitting of the single shot spectra to the theoretical rotational Stokes spectra of N2 and O2. The laser employed in this study was a high energy, long-pulsed, frequency doubled Nd:YAG laser. One thousand single-shot spectra were acquired at each spatial coordinate. Mean temperature and rms temperature variations were calculated at each measurement location. Excellent agreement between the averaged and single-shot temperatures was observed with an accuracy better than 2.5% for temperature, and rms variations in temperature between ±2.2% at 296 K and ±4.5% at 850 K. The mean and normalized rms temperatures measured here were then compared to NASA’s Consensus data set of PIV velocity and turbulence measurements in similar jet flows. The results of this and planned follow-on studies will support NASA GRC’s development of physics-based jet noise prediction, turbulence modeling and aeroacoustic source modeling codes.

Imaging flow during impingement of differentially heated jets over a flat surface

The present study investigates thermal fluctuations occurring in the mixing region of two adjacent differentially heated water jets impinging on a horizontal stainless steel surface. The nozzle diameters of the individual jets are equal. The jets are immersed in a pool of water at the ambient temperature. The Reynolds number range considered in the experiments is 2.09×103–2.51×104 for each jet, while the Richardson number is in the range of 9.58×10−3–1.38×10−2. Light intensity fluctuations in the interfacial region of the jets are imaged using the shadowgraph technique. Particle image velocimetry (PIV) has been carried out in a plane passing across the two jets. The effect of various flow rates near the nozzles and the impingement plate are visualized. Time-averaged and RMS temperature fluctuations on the exposed face of the impingement plate are measured using thermocouples. Spectra of light intensity fluctuations determined from the shadowgraph data are correlated with those in wall temperature.Light intensity spectra grow in amplitude in the flow direction, as additional jet instabilities set in. The spectra are broadband with distinct peaks, typical of high Reynolds number jets. Time-averaged and RMS wall temperature distribution are quite distinct from those of light intensity within the impinging jets. Consistent with a wall-jet behavior, the largest RMS wall temperature occurs near the stagnation point and decays away from it. The gradient in the time-averaged wall temperature is the highest for equal velocity jets and occurs at the mid-plane location. This is also the location of the peak in RMS wall temperature. Among all velocity ratios, the equal velocity configuration shows the highest RMS wall temperature. Here, PIV imaging shows a recirculation pattern in the time-averaged velocity near the stagnation point. When the flow rates are unequal, the higher velocity jet provides a blanket on the lower velocity side. The wall temperature fluctuations depend on the interaction between the cold and the hot jets and the location of the impingement plate.JEL Classification: K. Thermal hydraulics

Large eddy simulation of a premixed propane turbulent bluff body flame using the Eulerian stochastic field method

A premixed propane/air flame stabilized on a triangular bluff body was studied by numerical simulation as a simplified model of many practical propulsion and power generation systems. The sub-grid scale (sgs) probability density function (pdf) approach in conjunction with the stochastic fields solution method is used to account for sgs turbulence–chemistry interactions; a skeleton chemistry mechanism with 4 reaction steps and 7 species was used to describe the propane–air reaction. Three cases, one non-reacting and two reacting were studied. The instantaneous flow pattern and CO concentration are discussed and the averaged velocity and temperature, the RMS velocity and temperature fluctuations and averaged CO mass fraction profiles are compared with the experimental data. The simulations show very good agreement with the experimental data demonstrating the capability of the LES method coupled with the sgs-pdf method in representing premixed combustion in complex flame configurations.

THEORY AND SIMULATIONS OF ROTATING CONVECTION

We study thermal convection in a rotating fluid in order to better understand the properties of convection zones in rotating stars and planets. We first derive mixing-length theory for rapidly-rotating convection, arriving at the results of Stevenson (1979) via simple physical arguments. The theory predicts the properties of convection as a function of the imposed heat flux and rotation rate, independent of microscopic diffusivities. In particular, it predicts the mean temperature gradient; the rms velocity and temperature fluctuations; and the size of the eddies that dominate heat transport. We test all of these predictions with high resolution three-dimensional hydrodynamical simulations of Boussinesq convection in a Cartesian box. The results agree remarkably well with the theory across more than two orders of magnitude in rotation rate. For example, the temperature gradient is predicted to scale as the rotation rate to the 4/5th power at fixed flux, and the simulations yield $0.75\pm 0.06$. We conclude that the mixing length theory is a solid foundation for understanding the properties of convection zones in rotating stars and planets.

Large-Eddy Simulation/Reynolds-Averaged Navier–Stokes Simulations of High-Speed Mixing Processes

A large-eddy simulation/Reynolds-averaged Navier–Stokes model is applied to three high-speed mixing layers and three sonic injection flows to generate data suitable for evaluating two current Reynolds-averaged Navier–Stokes models for turbulent mass diffusivity. These models solve transport equations for concentration variance and dissipation rate and differ in the constitutive relation for the turbulent mass diffusivity and the form of the evolution equation for the dissipation rate. The predictive capability of the large-eddy simulation/Reynolds-averaged Navier–Stokes model is assessed through simulations of an air–air mixing-layer experiment and a sonic ethylene injection into a Mach 2.0 airstream. This model provides good predictions of the mean velocity, turbulence intensity, and rms temperature fluctuation throughout the shear layer flowfield but slightly over-predicts the spreading rate of the mixing layer. The simulation of the sonic injection is in generally good agreement with the experiment but underpredicts the level of jet entrainment. Four other large-eddy simulation/Reynolds-averaged Navier–Stokes data sets, involving the replacement of the lower airstream in the mixing-layer configuration by an argon stream and a helium stream, and a replacement of the injectant gas in the sonic injection experiment with argon and helium are also generated. All data sets are “mined” to extract turbulent mass diffusivities, concentration variances, and scalar dissipation rates associated with the resolved eddy motion. The results show that both models can be optimized to achieve a good match with the exact scalar variance production rate.

The energy of waves in the photosphere and lower chromosphere

Most static 1D atmosphere models in the quiet Sun predict a rise of the gas temperature at chromospheric layers, but numerical simulations only yield an increase in the brightness temperature. We investigate the thermal structure in the solar chromosphere as derived from an LTE inversion of Ca II H spectra in QS and active regions. We investigate the temperature stratifications on differences between magnetic and field-free regions in the QS, and between QS and ARs. We determine the energy content of individual calcium bright grains (BGs). The rms temperature fluctuations are below 100 K in the photosphere and 200-300 K in the chromosphere. The average temperature stratification in the QS does not exhibit a clear chromospheric temperature rise, opposite to the AR case. We find an energy content of about 7*10E18 J for BGs that repeat with a cadence of about 160 secs. The precursors of BGs have a vertical extent of about 200 km and a horizontal extent of about 1 Mm. The comparison of observed with synthetic NLTE profiles confirms that the solar chromosphere in the QS oscillates between an atmosphere in radiative equilibrium and one with a moderate chromospheric temperature rise. Two-dimensional x-z temperature maps exhibit nearly horizontal canopy-like structures with a few Mm extent around photospheric magnetic field concentrations at a height of about 600 km. The large difference between QS regions and ARs, and the better match of AR and non-LTE reference spectra suggest that magnetic heating processes are more important than commonly assumed. The temperature fluctuations in QS derived by the LTE inversion do not suffice on average to maintain a stationary chromospheric temperature rise. The spatially and vertically resolved information on the temperature structure allows one to investigate in detail the topology and evolution of the thermal structure in the lower solar atmosphere.

Astrophysical dust formation under the influence of temperature fluctuations

Context. Dust formation, i.e. the condensation of solid particles from a gas phase, occurs in astrophysical environments that are sufficiently cool and offer a sufficiently high density of condensable species. Since many astrophysical systems in which dust forms have turbulent features and the dust formation rates depend significantly on temperature, we investigate the influence of temperature fluctuations on dust condensation in dust-driven AGB winds. Aims. We present an approach for the time-dependent stochastic description of astrophysical dust formation and apply this in developing a fast algorithm, which is well suited for implementation into numerical models of dynamical AGB winds. The influence of the fluctuations on the dynamical structure is then investigated for a large sample of wind parameters. Methods. We employ a mathematical method, which describes the dust formation under the influence of random temperature fluctuations as a stochastic process. A system of Fokker-Planck equations for the one-point distribution function of the conjoint temporal development of temperature and dust results. Gas-box studies of this system have led us to a simplified microturbulent description for the implementation into time-dependent numerical wind models. Results. A method for the investigation of temperature fluctuations on dust formation is presented, which can be adapted to a variety of astrophysical situations. For dust-driven AGB winds, a microturbulent description turns out to be admissible. In AGB winds, rms-temperature fluctuations of 20–60 K can result in increased mass loss rates of 10–30% depending on the details of the physical model assumptions. Conclusions. The presented method for the treatment of temperature fluctuations with respect to dust formation has been succesfully applied to dynamical AGB winds. We suggest how to apply the method to other astrophysical systems. The influence of the fluctuations on the dynamics of dust-driven AGB winds is remarkable, but not overwhelming.

Structure of the thermal boundary layer for turbulent Rayleigh-Bénard convection of air in a long rectangular enclosure

Measurements of the temperature distribution were performed in the upper (cold) boundary layer of a rectangular Rayleigh-Bénard cell with aspect ratios Gamma(x) = 5 and Gamma(y) = 1 using air with Prandtl number Pr = 0.71 as the working fluid. The range of investigated Rayleigh numbers was from Ra approximately 6 x 10(7) to Ra approximately 6 x 10(8), and the measurements were taken at two different positions with the purpose of understanding the variation of the properties of the thermal boundary layer along the cell. We present profiles of the mean temperature, rms temperature fluctuations, skewness, and kurtosis as a function of the distance from the cooling plate from which we extract scaling exponents and boundary layer thicknesses. Whereas most of these quantities are found to depend monotonically on the Rayleigh number for the peripheral measurement position, their values at the central measurement position exhibit a high degree of variability. These observations indicate that the properties of the thermal boundary layer in large-aspect-ratio convection can have strong spatial variations.

Turbulent thermal boundary layer on a permeable flat plate

Scaling laws are established for the profiles of temperature, turbulent heat flux, rms temperature fluctuation, and wall heat transfer in the turbulent boundary layer on a flat plate with transpiration. In the case of blowing, the temperature distribution represented in scaling variables outside the viscous sublayer has a universal form known from experimental data for flows over impermeable flat plates. In the case of suction, the temperature distribution is described by a one-parameter family of curves. A universal law of heat transfer having the form of a generalized Reynolds analogy provides a basis for representation of the heat flux distributions corresponding to different Reynolds numbers and transpiration velocities in terms of a function of one variable. The results are obtained without invoking any special closure hypotheses.

Lyman forest-CMB cross-correlation and the search for the ionized baryons at high redshift

The intergalactic neutral hydrogen, which is responsible for the Lya forest of quasar absorption lines, is a tracer of much larger amounts of ionized hydrogen. The ionized component has yet to be detected directly, but is expected to scatter cosmic microwave background (CMB) photons via the Sunyaev-Zel'dovich effect. We use hydrodynamic simulations of a A cold dark matter (CDM) universe to create mock quasar spectra and CMB sky maps from the same volume of space. We find that the high-redshift Lya forest gas causes temperature fluctuations of the order of 1 μK rms in the CMB on arcmin scales. The kinetic and thermal Sunyaev-Zel'dovich effects have a similar magnitude at redshift 3, with the thermal effect becoming relatively weaker as expected at higher redshift. The CMB signal associated with lines of sight having H I column densities >10 18 cm -2 is only marginally stronger than that for lower column density sightlines. There is a much more significant dependence of rms temperature fluctuation on mean Lya absorbed flux, however, suggesting that the CMB signal effectively arises in lower density material. We investigate the extent to which it is possible to cross-correlate information from the Lya forest and the microwave background to detect the Sunyaev-Zel'dovich effect at redshifts 2-4. In so doing, we are able to set direct limits on the density of diffuse ionized intergalactic baryons. We carry out a preliminary comparison at a mean redshift z = 3 of 3488 quasar spectra from Sloan Digital Sky Survey (SDSS) Data Release 3 and the WMAP first year data. Assuming that the baryons are clustered as in a ACDM cosmology, and have the same mean temperature, the cross-correlation yields a weak limit on the cosmic density of ionized baryons Ω b,I . As a fraction of the critical density, we find Ω b,I < 0.8 at 95 percent confidence. With data from upcoming CMB telescopes, we anticipate that a direct detection of the high-redshift ionized intergalactic medium will soon be possible, providing an important consistency check on cosmological models.

Direct numerical simulation of momentum and heat transport in idealized Czochralski crystal growth configurations

Turbulent momentum and heat transport in idealized Czochralski crystal growth configurations is investigated by means of direct numerical simulation. The analysis of the flow data focuses on the influence of crystal and crucible rotation on the flow structures and the development of temperature fluctuations. A numerical parameter study is performed to investigate how the variation of the numerous flow parameters affects the turbulent transport processes. Finally, a direct numerical simulation is conducted with parameters taken from experiment in order to allow a direct comparison between numerical and experimental results. It is found that counter-rotation of the crystal and crucible leads to a complex flow, which is characterized by three major recirculation zones, if crucible rotation dominates the flow. The dynamics of the flow are controlled by centrifugal forces counteracting buoyancy and surface tension effects. High temperature fluctuations are created within or close to the crystallization zone. Neither a variation of the melt height, nor a reduction of the crystal rotation rate or a change of the Grashof and Marangoni numbers has a major effect on the bulk flow structure and overall heat transfer. Increasing rotation of the crystal changes the bulk flow structure strongly and leads to an increased value of maximum rms temperature fluctuations, the position of which is shifted towards the crucible bottom. A shifted position of maximum rms temperature fluctuations is also observed if heat radiation across the free surface is taken into account.

Numerical Analysis of Compressible Turbulent Channel Flow with Wall-Temperature Difference

The objective of this study is to clarify the effect of different thermal wall boundary conditions on turbulence statistics and structures in the compressible turbulent flow. We performed direct numerical simulation (DNS) of the compressible turbulent channel flow between isothermal walls with temperature difference (Case C1). The DNS data was compared with that of the compressible turbulent channel flow between adiabatic and isothermal walls (Case C2), and that of the incompressible turbulent channel flow between isothermal walls with temperature difference (Case I). The main results are as follows : (1) The mean velocity in the logarithmic region and the maximum of the RMS streamwise velocity fluctuation in wall units are smaller than those of Case I near the high temperature isothermal wall, while they are larger than those of Case I near the adiabatic wall. (2) Near the high temperature isothermal wall, the mean temperature profile has an additional maximum due to the friction work, and the RMS temperature fluctuation has the corresponding maximum. This is consistent with the fact the production term of temperature variance has the additional maximum in the region very close to the high temperature isothermal wall. (3) The correlation coefficient between streamwise velocity and temperature fluctuations of Case C1 is significantly different from those of Cases C2 and I in the region very close to the high temperature wall. (4) The direction of energy transfer due to pressure work near the high temperature isothermal wall is the same as that of near the adiabatic wall. (5) The compressible terms of the temperature variance transport equation are not negligible near the low temperature isothermal wall.

Small‐Scale Cosmic Microwave Background Temperature and Polarization Anisotropies Due to Patchy Reionization

We study contributions from inhomogeneous (patchy) reionization to arcminute-scale (1000 < l < 10,000) cosmic microwave background (CMB) anisotropies. We show that inhomogeneities in the ionization fraction, rather than in the mean density, dominate both the temperature and the polarization power spectra. Depending on the ionization history and the clustering bias of the ionizing sources, we find that rms temperature fluctuations range from 2 to 8 μK and the corresponding values for polarization are over 2 orders of magnitude smaller. Reionization can significantly bias cosmological parameter estimates and degrade gravitational lensing potential reconstruction from temperature maps but not from polarization maps. We demonstrate that a simple modeling of the reionization temperature power spectrum may be sufficient to remove the parameter bias. The high-l temperature power spectrum will contain some limited information about the sources of reionization.

Quantitative temperature imaging in gas-phase turbulent thermal convection by laser-induced fluorescence of acetone

In this paper, an acetone planar laser-induced fluorescence (PLIF) technique for nonintrusive temperature imaging is demonstrated in gas-phase (Pr = 0.72) turbulent Rayleigh–Bénard convection at Rayleigh number Ra = 1.3×105. The PLIF technique provides quantitative spatially correlated temperature data without the flow intrusion or time lag associated with physical probes, and without the significant path averaging that plagues most optical heat-transfer diagnostic tools, such as the Mach–Zehnder interferometer, thus making PLIF an attractive choice for quantitative thermal imaging in easily perturbed, complex three-dimensional flow fields. The "instantaneous" (20-ns integration time) thermal images presented have a spatial resolution of 176×176×500 µm and a single-pulse temperature measurement precision of ± 2.5 K, or 2.5% of the total temperature difference. These images represent a two-dimensional slice through a complex three-dimensional flow, allowing for thermal structure of the turbulence to be quantified. Statistics such as the horizontally averaged temperature profile, root-mean square (rms) temperature fluctuation, two-point spatial correlations, and conditionally averaged plume structures are computed from an ensemble of 100 temperature images. The profiles of the mean temperature and rms temperature fluctuation are in good agreement with previously published data, and the results obtained from the two-point spatial correlations and conditionally averaged temperature fields show the importance of large-scale coherent structures in this turbulent flow.

Radio Point Sources and the Thermal Sunyaev‐Zeldovich Power Spectrum

Radio point sources are strongly correlated with clusters of galaxies, so a significant fraction of the thermal Sunyaev-Zeldovich (SZ) effect signal could be affected by point-source contamination. Based on empirical estimates of the radio galaxy population, it is shown that the rms temperature fluctuations of the thermal SZ effect could be underestimated by as much as 30% at an observing frequency of 30 GHz at l ≳ 1000. The effect is larger at higher multipoles. If the recent report of excess power at small angular scales is to be explained by the thermal SZ effect, then radio point sources at an observing frequency of 30 GHz must be a surprisingly weak contaminant of the SZ effect for low-mass clusters.