The thermal inertia of sensors drastically limits the measurement of the temperature fluctuations in the high-frequency range. This issue is often addressed using cold wire techniques with dedicated corrections. In this study, three methods are employed to compensate high-frequency attenuation, and the correction of the end losses, are evaluated for four wires with different aspect ratios and diameters. The fidelity of the corrected measurements is assessed by comparing the spectra of temperature fluctuations obtained with the cold wires operating in a constant voltage circuit, to those derived from optical measurements. The latter method is based on Rayleigh scattering and is in principle not affected by thermal inertia as it relies on molecular light scattering. Two flows presenting high levels of temperature fluctuations are considered. Namely, the wake of a heated cylinder, and a mixing layer between two jets in co-flow and at different temperatures. These two configurations allow exploring cold wire performances at high frequency, and show that precise measurements can be performed up to 10 kHz with a wire $$1\,\upmu \hbox {m}$$ in diameter.

The knowledge of temperature fluctuations is essential for most thermoacoustic systems. In the present paper, cold wire constant-voltage anemometry (CVA) to measure temperature fluctuations is presented. Corrections for the thermal inertia and for the end losses of the wire are applied during the post-processing. The correction for the thermal inertia of the cold wire is achieved by applying a time dependent thermal lag as proposed originally for a constant-current anemometry (CCA) system. This thermal lag is measured in parallel by a hot wire. The thermal end losses of the wires to their supports are also considered and approximate corrections are proposed. The procedure for the cold wire CVA is validated in the acoustic field of an acoustic resonator with wires of different lengths. A comparison between a CVA and a CCA measurement also confirms the CVA measurement. Furthermore, the proposed measurement procedure is applied close to the stack of a thermoacoustic refrigerator. Supposing a two-dimensional flow, the simultaneous measurement of velocity and temperature fluctuations is possible. This allows a detailed examination of the acoustic field close to the stack, including the study of the correlation between temperature and velocity.

Hot-wire and hot-film anemometers are devices used to measure the variables. occurring in turbulent flows, such as meanand fluctuating-velocity components, mean and fluctuating temperature, etc. The sensors are thin metallic elements heated by an electric current (Joule effect) and cooled by the incident flow, which acts by virtue of its mass flux and its temperature (through various effects, but with forced convection usually predominant). From the temperature (or resistance) attained by the sensor, it is then possible to deduce information on the flow. More than one sensor, or more than one value of the heating current, is often necessary to investigate thoroughly a turbulence field.

This first chapter illustrates the interest of turbulent flows. Numerous definitions and general concepts are introduced to characterize turbulence. Some practical consequences are also briefly described. On the whole, transport is very efficient in a turbulent flow, be it for momentum, mass or heat. Nonetheless, with this efficiency comes an increase in wall friction which is rarely sought. A few examples of the advantages and drawbacks of the turbulent regime are given.

This chapter focuses on turbulent models, which are widely used in a large variety of engineering studies, including atmospheric dynamics and weather forecasting. The objective is to determine the turbulent mean flow from the averaged equations ( 2.14 ) and ( 2.15 ) established in Chap. 2. A turbulence model is however required to express the unknown Reynolds stress tensor. The most popular approaches are based on Boussinesq’s hypothesis ( 2.24 ) with the introduction of a turbulent viscosity. A survey of these so-called eddy-viscosity models is presented in this chapter.

In this chapter, self-similar solutions of free subsonic jets and wakes are established. These solutions can be used to characterize some properties of the mean turbulent flow itself, to assess turbulence models, and also to provide an analytical solution for the mean flow field under some assumptions. The development of a round jet flow is first described, results for a plane jet are then briefly reported, round and plane wake flows are then examined in the two last sections.

Wall turbulent flows are constrained by the presence of at least one rigid wall, which imposes a no-slip boundary condition at its surface.

An overview of high-fidelity numerical simulation techniques is presented in this chapter. Advantages and limitations are discussed for research or engineering purposes. These time-dependent approaches are distinguished from mean flow calculations based on the averaged Navier-Stokes equations, which are examined in Chap. 9 .

The development of high-performance thermoacoustic systems requires efficient heat transfer between the stack or the regenerator and the heat-exchangers. So far, the coupling between these elements has been addressed using theoretical models and numerical simulations1. These analyses demonstrate that, at the high acoustic levels found in realistic thermoacoustic systems, acoustic velocities and instantaneous temperatures exhibit nonlinear interactions. However, there is a lack of controlled experimental data to validate these results. In this paper we consider a standing-wave thermoacoustic refrigerator. It consists of a stack of plates placed in an acoustic resonator. Two heat exchangers are located at each stack extremity. The thermoacoustic effect takes place in the thermal and viscous boundary layers along each plate of the stack. It results in a heat transport along the plates and in a temperature difference between the two stack ends. The full understanding of the heat transfer between the stack and the heat exchangers is a key issue to improve the global efficiency of these devices.

This chapter focuses on the statistical approach to turbulence. On the one hand, it seeks to describe the evolution of mean and turbulent fields, and on the other, to highlight the transfer terms between these two fields.

A detailed procedure to use a constant-voltage anemometer (CVA) for the accurate measurement of turbulent flows is proposed. The procedure is based on the usual small-perturbation analysis of hot-wire signals. It consists in three steps: (1) the calibration of internal elements, required to estimate the two main electrical parameters of the CVA circuitry that are needed in the data analysis, (2) a flow calibration to relate the CVA output voltage and the hot-wire time constant to the flow velocity, and (3) a data-processing algorithm to recover the fluctuating flow quantities from the output voltage. The procedure is tested in two classical turbulent flows: a zero-pressure-gradient boundary layer and a round jet. In both cases, the CVA results are shown to be essentially indistinguishable from the results obtained with a research-grade constant-temperature anemometer.

It has been shown in Chap. 6 how the description of an isotropic turbulent field can be simplified for an incompressible flow. In physical space, only one scalar function $$f(r)$$ is necessary to describe the two-point velocity correlations $$R_{ij}({\varvec{r}})$$ . In the Fourier space, only the turbulent kinetic energy spectrum $$E(k)$$ is necessary to describe the corresponding velocity spectral tensor $$\phi _{ij}({\varvec{k}})$$ . In this chapter, we consider how these functions $$E(k)$$ and $$f(r)$$ evolve with time in a decaying turbulent field.

A statistical approach to turbulence was adopted in Chap. 2 , in which averaged Navier-Stokes equations were considered.

The nonlinear behavior of constant-temperature anemometers is investigated experimentally and numerically for three commercially available anemometers. The experiments are performed in the potential core of a subsonic jet by injecting electrical signals of varying amplitudes and frequencies in the hot wire and recording the anemometer output signals. The numerical model is based on Freymuth’s theoretical analysis (1977 J. Phys. E: Sci. Instrum. 10 705–10). The two approaches are in good agreement, which demonstrates the validity of Freymuth’s nonlinear theory of constant-temperature anemometers. The results confirm that significant errors are made in the third-order turbulence moment, also called the skewness factor, when the amplitude of velocity fluctuations is large and their frequency is not small compared to the cut-off frequency of the system.

Durham University, School of Engineering and Computing Sciences, Science Site, South Road, DH13LE Durham, UK Laboratoire d’acoustique de l’université du Maine, Bât. IAM UFR Sciences Avenue Olivier Messiaen 72085 Le Mans Cedex 9 Laboratoire de Mecanique des Fluides et d’Acoustique, 36 Av Guy de Collongue 69134 Ecully Cedex arganthael.berson@durham.ac.uk Proceedings of the Acoustics 2012 Nantes Conference 23-27 April 2012, Nantes, France

The nonlinear temperature field in the vicinity of the stack of a standing-wave thermoacoustic refrigerator is investigated both theoretically and experimentally. First, the problem is addressed theoretically by a one-dimensional nonlinear model that predicts the generation of thermal harmonics near the ends of the stack. The model relies on a relaxation-time approximation to describe transverse heat transfer between the stack walls and the working fluid. It extends a previous model proposed by [Gusev et al., Thermal wave harmonics generation in the hydrodynamical heat transport in thermoacoustics, J. Acoust. Soc. Am. 109 (2001) pp. 84–90], by including the effect of axial conduction on temperature fluctuations. Second, the nonlinear temperature field is investigated experimentally. The amplitude of temperature fluctuations behind the stack at the fundamental frequency and second harmonic are measured using cold-wire anemometry. The measurements rely on a procedure recently developed by the authors that allows a full correction of the thermal inertia of the sensor. Experimental results are in good agreement with the predictions of the model. The generation of thermal harmonics behind the stack is thus validated. The influence of the Péclet number on the thermal field, which depends on the diffusivity of the working fluid and on the acoustic frequency and pressure level, is also demonstrated.