PRESSURE DISTRIBUTION IN SEPARATION REGION OF TURBULENT PULSATING FLOW

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1 PRESSURE DISTRIBUTION IN SEPARATION REGION OF TURBULENT PULSATING FLOW N.I.Miheev, I.A.Davletshin, D.I.Romanov Power Engineering Department, Kazan Science Center, Russian Academy of Sciences Kazan, 4111, Russia The reattachment length is one of the most important characteristics of separated flows. Reattachment point is usually defined as a point with zero value of streamwise component of the skin friction vector or as a point at which forward and backward flows are equiprobable [1]. Skin friction measurements demand considerable efforts. Hence, information on static pressure distribution along the separation region can be used for reattachment length estimations. In this paper some experimental results concerning hydrodynamic parameters of turbulent separated flow with superimposed flow rate fluctuations: distributions of streamwise component of the skin friction vector, axial velocity and static pressure along the separation region are obtained (fig.1). Fig.1. Separated flow in axisymmetric channel The experiments were conducted in an axisymmetric duct with diameter of D=64 mm and length of 468 mm (fig.). Relatively short channel was chosen in order to avoid resonance effects and at the same time to provide the length significantly exceeding the separation region. Superimposed airflow rate fluctuations were generated by rotating flap 3 periodically overlapping the flow section at the pipe outlet. Thus, the law of velocity variation was guaranteed to be close to harmonic one: U = U +A U sin(π f t + φ), where U and A U are mean value and amplitude of velocity, t time, φ initial phase. The flow separated from an orifice edge with diameter of d=4 mm located at the pipe inlet. Frequency of superimposed airflow rate fluctuations was within the range of f=-377 Hz. Longitudinal component of the skin friction vector τ х was measured with the help of a hot-wire probe 4 and apparatus DISA-55M. Static differential pressure between cross-sections I and II was measured using measuring devices PROMA-IDM. Simultaneously instantaneous velocity (at the channel's axis) at these crosssections was observed. Construction of the channel including rings of various length (; 4; 6; 1 mm) gave a capability to move a test section I with a skin friction vector probe and a pressure tap along the channel with a step of mm. The test section II was fixed at the outlet of the channel. The experiments are described in a more detailed way in []. N.I. Miheev, I.A. Davletshin, D.I. Romanov, 8

2 Fig.. Experimental setup The experiments were conducted at the values of mean-flow-rate velocity in a pipe (downstream the reattachment point) equal to U =4,6-16,6 m/s (Re=U D/ν=(,3-8,) 1 4 ). Relative amplitude A U /U of superimposed velocity fluctuations measured by the hot wire at the channel axis behind the orifice above the separation region reached the value of,4.,,1,,1,, -,1 -, Гц , а -,1 -, -,3 Гц b,1,5, -,5 -,1 -,15 Гц Fig.3. Distribution of longitudinal component of skin friction vector: а U =4.6 m/s; b U =8. m/s; c U =16.6 m/s c

3 Experimental distributions of the longitudinal component of the skin friction vector are obtained (fig.3). Obviously, the plots are segregated according to the frequencies of imposed pulsations. In particular the coordinate of the zero value of τ х was different at various frequencies, i.e. the reattachment length varied depending on the frequency. So, the reattachment length X R at various pulsating regimes was determined using obtained distributions of τ х along the channel. The effect of separation region abrupt decrease depending on frequency was revealed (fig.4). x R /h 1 Re=U D/ν=.3x x1 4 8.x Sh=fX R /U Fig.4. Length of separation region behind orifice with diameter of d=4 mm in pulsating flow Experimental distributions of static pressure drop between the sections in the separation and relaxation regions are plotted in fig.5. Here pressure drop coefficient is с P =ΔP/(ρ U /), where ΔP pressure drop between the current section and the fixed section at the pipe end. Fig.5 shows that plots are segregated according to their frequencies, i.e. the plot behavior is similar to behavior of longitudinal component of the skin friction vector distributions. Characteristic pressure value at flow reattachment (fig.6) was calculated using the length of separation region (fig.4) and static pressure distribution (fig.5) in a pulsating flow.

4 - Гц Гц а b c Гц Fig.5. Static pressure distribution: а U =4.6 m/s; b U =8. m/s; c U =16.6 m/s Despite the significant shift of the mean reattachment point behind the obstacle in a circular pipe depending on the frequency of superimposed fluctuations (fig.6) the value of pressure (relative to minimum and maximum of a distribution) at this point remains approximately constant and is equal to Р XR -P min (.7...8)(P max -P min ). The obtained results give a possibility to define reattachment point coordinates in a pulsating flow using the pressure distribution in the separation region. 1, (P XR -P min )/(P max -P min ),8,6,4 Re=U D/ν=.3x x1 4 8.x Sh=fX R /U Fig.6. Static pressure at reattachment point

5 This work was supported by Russian Foundation of Basic Research (grants , , ) and by grant of the President of the Russian Federation (grant NSh ). Literature 1. Kozlov A.P., Miheev N.I., Molochnikov V.M., Saykin A.K. Characteristics of skin friction vector in turbulent separated and reattaching flows // Izvestia RAN. Energetika No.4.- P Miheev N.I., Davletshin I.A., Fashutdinov R.E., Dushina O.A. Separation region in pulsating flow behind orifice // XVI School-seminar of young scientists and specialists under guidance of Academician A.I. Leontiev Problems of Gas-Dynamics and Heat- Mass Exchange in Energy Plants, May Sankt- Peterburg, 7.- Vol.1.- Pp