The vorticity formed in the cross section of a turbulent flow in a straight circular pipe rotating about its longitudinal azis decreases the values of the turbulent stresses, turbulence energy, and dissipation rate along the pipe. The results of laboratory ezperiments and calculations by the second-order closure model of turbulent transfer are presented. On the whole, the model using a system of transport equations yields better agreement with ezperimental data than the models with algebraic relations for second-order moments.Introduction. The action of mass forces in a swirling flow (centrifugal and Coriolis accelerations), which is similar to the action of the acceleration of gravity in a stratified flow [1, 2], weakens momentum and heat-transfer processes. The vorticity formed in the cross section of a turbulent flow in a straight circular pipe rotating about its longitudinal axis suppresses turbulent fluctuations and radial turbulent transfer at small and moderate velocities of pipe rotation: the turbulent stress, the turbulence energy, and its dissipation decrease.Onufriev and Khristianovich [3, 4] considered the influence of the swirling flow on its statistical characteristics on the basis of semi-empirical equations that describe the behavior of the mean velocity fields and the second-order moments in the local-equilibrium approximation.We present the data of laboratory measurements of the first-and second-order moments of the velocity field for a flow of an incompressible liquid in a motionless and rotating pipe. These data are compared with the calculation results obtained using three models of turbulent transfer. These models include differential transport equations for the components of the Reynolds stress tensor, algebraic relationships for normal turbulent stresses in the nonequilibrium approximation, and algebraic relationships for turbulent stresses in the local-equilibrium approximation, respectively.The experimental hot-wire anemometry results were obtained at the Moscow Physicotechnical Institute, and the calculations were performed at the Institute of Theoretical and Applied Mechanics of the Siberian Division of the Russian Academy of Sciences and Novosibirsk State University.Experimental Study of the Turbulent Flow Characteristics in a Rotating Pipe. The experiments were performed on a setup whose main units were the straight section of a channel whose length was equal to 100 diameters and which formed a developed turbulent flow and the rotating section, which was 25 diameters long (the channel diameter was 0.06 m). The air was injected into the channel from a high-pressure pipeline through a reductor and a flow governor, which ensured a constant flow rate. The temperature of the air injected into the channel was maintained constant and equal to room temperature by means of an automatically adjusted heater. After the heater, the air entered a receiver wherein it passed

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An analysis of experimental results on the behavior of spectra corresponding to the diagonal components of the Reynolds stress tensor [1] and a consideration of the similarity properties of a generalized model of the spectrum of an isotropic flow [2, 3] demonstrate the existence of a more or less universal representation for these spectral distributions. In the energy-significant interval the wavenumber is normalized to the longitudinal integral correlation scale. Nonuniformity and anisotropy of the flow introduce systematic deviations into the spectral distributions.The use of the integral scale as a characteristic length of similarity is built into the yon Karman equation [4] and in Rotta's derivation [4] of the transport equation for the integral correlation scale. An intriguing topic in connection with this problem is the behavior of the spectra corresponding to higher moments. Here we investigate the third moments measured by a hot-wire anemometer using an x-shaped probe.The measurements were carried out for fully developed turbulent flow in a straight pipe of diameter 0.06 m at an axial velocity of 10 m/sec; the kinematic viscosity was v = 1.4.10 -5 m2/sec, and the Reynolds number determined from the average velocity was Re = 3.47-104 . The friction velocity vf = 0.433 m/sec was determined from curves plotted for fully developed pipe flow [6]. The apparatus and methodological considerations are discussed in [7][8][9]. A standard R61 sensor with two filaments of length l = 1.2.10 -3 m and standard DISA hardware units were used; the signals were recorded on a digital tape recorder and were processed on a Plurimat-S computer. Special processing programs were developed to encompass the entire dynamic spectral range. The characteristics of the linearizers were selected with a view toward creating identical linear dependences for both filaments. The velocity-voltage conversion nonlinearity did not exceed 1%. The sensitivity was chosen on the basis of the condition that a signal attaining four standard deviations should be transmitted without distortion.The fast Fourier transform and a procedure described in [10] are used to estimate the spectrum. The number of realizations is M = 1024 (sometimes 256), each m-th realization has a duration T (N = 2048 readings in a realization). The discretization frequency is fl = 5000 Hz. A smoothing Hannah window is used. The one-sided cross-spectral densities are obtained by averaging over all realizations:

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1. Formulation of the Problem. One method of closing the system of equations describing turbulent flow is that of using the relation between the fourth-and second-order correlation moments according to the hypothesis of zero values of fourth-order cumulants [1, 2]:(the subscripts refer to the first time point and the superscripts to the second). The same hypothesis can be expressed in terms of the Fourier transforms corresponding to the fourth-and second-order moments [2, 3]:--00 --00The true probability-density distribution of velocity fluctuations is substituted by a model probability density function that could be yet a good approximation for calculating certain moments if the region of its negative values has little effect on the results of calculating these moments.Millionshchikov's hypothesis was experimentally verified in [4] for isotropic flow behind a grid. The experimental data were found to satisfy this hypothesis within the measurement error.The present paper is aimed at comparing experimental relations for developed turbulent pipe flows. 2. Experimental Setup and Measuring Equipment. The setup channel is a straight-line round pipe with diameter d = 0.06 m. The first part of the channel 6 m long is immovable and serves to form a developed symmetric turbulent flow that corresponds to a specified Reynolds number. The second part of the channel 1.5 m long can be rotated around the longitudinal axis. The flow is created by the air supply from a high-pressure pipeline through a heater and a receiver with a converging nozzle (contoured according to Vitoshinskii's relation) which ensures a flow-contraction ratio of 1 : 12. The room temperature is maintained in flow within 0.1 ~ The flow temperature is controlled by the thermocouple connected to a VK 2-20 voltmeter.Hot-wire anemometer equipment of DISA Company (series M) was used to measure the flow velocity. Signal linearization was performed. A 55P 11 straight general-purpose probe (wire length 1.25 mm and diameter 5 #m) was placed at various distances from the axis along the horizontal radius ~ of the cross section of the pipe. The wire was directed vertically along" the circumferential component of the flow velocity. The probe is not sensitive to the velocity component along the wire. Therefore, only the signal from the velocity component normal to the wire is taken into account. The wire was placed at a distance of 15 mm from the exit section inside the pipe ~1.The time realizations of the signals were registered by a digital tape-recorder, and their processing was performed on a Plurimat-S computer. To obtain one value of the time correlation functions, 153,000 signal samples with a sampling frequency of 10 kHz were used.