Experimental and numerical evaluation of thermodynamic effect on naca0015 hydrofoil cavitation in hot water

Nội dung text: Experimental and numerical evaluation of thermodynamic effect on naca0015 hydrofoil cavitation in hot water

1. Vietnam Journal of Mechanics, VAST, Vol.43, No. 3 (2021), pp. 253 – 264 DOI: EXPERIMENTAL AND NUMERICAL EVALUATION OF THERMODYNAMIC EFFECT ON NACA0015 HYDROFOIL CAVITATION IN HOT WATER Anh Dinh Le1,∗ 1School of Aerospace Engineering, VNU-University of Engineering and Technology, 144 Xuan Thuy street, Cau Giay district, Hanoi, Vietnam ∗E-mail: anh.ld@vnu.edu.vn Received: 17 December 2020 / Published online: 04 August 2021 Abstract. In this study, the cavitation in hot water, which implies tight interaction of ther- modynamic effect, phase change phenomena, and flow behavior, was studied by a com- bination of experiment and numerical simulation. The experiment in water up to 90°C was performed in the high temperature and high-pressure water tunnel with NACA0015 as a cavitator. The temperature inside the cavity was measured using the high-accuracy thermistor probe. According to the result, the temperature depression in the cavity was increased proportionally with the increase of freestream temperature. The inverse ther- modynamic effect was observed with the increase of cavity length when temperature in- creased. The maximum temperature depression of about 0.41°C was measured in the water at around 90°C. The temperature drop was reasonably captured in simulation by coupling our simplified thermodynamic model with our cavitation model and governing equations. The tendency of temperature depression in the cavity agreed well with experi- mental data under different flow conditions. Keywords: cavitation, computational fluid dynamics, thermodynamic, NACA0015. 1. INTRODUCTION The thermodynamic effect, which easily appears in cryogenic or hot water, is known as the good effect for the hydraulic machine. When cavitation occurs, the latent heat for vaporization is absorbed from the surrounding liquid, thus surrounding liquid tem- perature is decreased. Since cavitation is mainly governed by saturated vapor pressure, which is proportionality to fluid temperature, evaporation is hard to occur. Thus, the cavitation is suppressed. Hence, to improve the performance of hydraulic machines, the effective use of the thermodynamic effect should be considered and should be clarified in the design of the hydraulic machine. Moreover, for fluids such as cryogenic liquids or hot water, the cavitation implies the complex interaction between thermodynamic effect, phase change, and flow behavior such as turbulence. © 2021 Vietnam Academy of Science and Technology
2. 254 Anh Dinh Le The cavitation experiment in water at 95°C was performed in a venturi nozzle by Petkovsel et al. [1,2]. The temperature distribution along the nozzle was measured using a high-speed IR thermography with the maximum temperature depression was of about 0.4°C. Yamaguchi et al. conducted the cavitation experiment on NACA0015 hydrofoil in water with wide range temperature [3]. The temperature depression was measured using the thermistor probes, in that the maximum temperature depression of 0.3°C was observed on the supercavitation condition at 80°C. These experiments indicate that the thermodynamic effect, which is normally negligible in water at room temperature, is visible in hot water cavitation. On the other hand, Cervone et al. conducted the cavitation experiment on NACA0015 hydrofoil in water up to 70°C [4]. The inverse thermodynamic effect was visualized in their experiment, where cavitation became longer and thicker when the freestream temperature increases. It shows that the thermodynamic effect on cavitation has not yet been clarified. Regarding Computational fluid dynamics (CFD), a homogeneous model is a power- ful tool for the numerical simulation of cavitation. Several numerical studies of the ther- modynamic effect on cavitation based on a homogeneous model have been conducted using two different approaches. 1) the indirect method, in that the saturated vapor pres- sure drop is modified without solving an energy conservation equation, and 2) the direct method, where the saturated vapor pressure is calculated based on the temperature field by solving an energy conservation equation. The first approach was proposed by Tsuda et al. [5], and was applied to different objects in cryogenic liquids or refrigerants. The latter approach was proposed by Hosangadi et al. [6]. They conducted the simulation of cav- itation in liquid nitrogen and liquid hydrogen on a 2-D tapered hydrofoil. An enthalpy conservation equation was solved along with the governing equation of the mixture. Al- though the temperature depression inside the cavity was reproduced, the temperature tendency was not matched the experimental data. A similar approach was then widely used in numerical simulation of thermodynamic effect on cavitation [7,8]. Anh et al. pro- posed a simplified thermodynamic effect model belong to the second approach, which was expressed in form of a mixture temperature equation [9, 10]. In this model, the heat transfer due to evaporation/condensation was explicitly appeared and was adjusted to suit the homogeneous model. A CFD calculation for cavitating flow on a 2-D tapered hydrofoil in cryogenic liquids was validated. A better temperature profile was repro- duced using this model compare with the existing numerical data by past researches for cryogenic liquids [6–8]. In this study, the cavitation in hot water, where the thermodynamic effect, phase change phenomena, and flow behavior are tightly coupled, is studied by combining the experiment and numerical simulation. The experiment is conducted in the high tem- perature and high-pressure water tunnel. The NACA0015 hydrofoil is selected as the cavitator. The temperature of the water is heated up to 90°C. The temperature difference between the cavity and freestream is measured using the high accuracy thermistor probe. The CFD simulation is then conducted and compared quantitatively with the experimen- tal data. This work aims to clarify the applicability of our simplified thermodynamic model, which has been successfully applied for cryogenics liquids, for the prediction of
3. Experimental and numerical evaluation of thermodynamic effect on NACA0015 hydrofoil cavitation in hot water 255 hot water cavitation. Moreover, the flow behaviors such as temperature effect and veloc- ity effect are emphasized. 2. MEASUREMENTS 2.1. Experimental setup The cavitation experiment in hot water was studied in high temperature and high- pressure water tunnels as on the left side of Fig.1. In this tunnel, the pressure can rise to 0.5 MPa, and the temperature can heat up to 140°C using an electric heater with an accuracy of 0.1°C. The test section is a channel with 30 mm × 20 mm in cross-section and 330 mm in length. An observation window, made of glass, was installed to test the section to enable the visualization of cavitation appearance. The tank pressure was con- trolled using a compressor and vacuum pump; the flow rate was adjusted by controlling the pump rotation speed. The upstream and downstream pressures of the object were measured using a pressure transducer. In this study, the NACA0015 hydrofoil with a chord length of 40 mm and 20 mm span width, which is based on Yamaguchi’s work [3], was used. The angle of attack was at 12 degrees. Two thermistor probes with high accu- racy (Nikkiso-Thermo Co., Ltd.) were inserted to the mid-span of the channel to measure the freestream temperature T0 (ThP1) and cavity temperature Tc (ThP2) as in the right Fig. 1. Overview of (left) high temperature – high pressure water tunnel and (right) the configu- ration of NACA0015 hydrofoil with two thermistor probes (the dimension is in mm)
4. 256 Anh Dinh Le side of Fig.1. These thermistor probes were calibrated using a TAKASAGO thermome- ter. The resistance of the thermistor probe was measured using a digital multimeter. The high-speed charged-coupled device (CCD) camera was used to visualize the cavity as- pect with a frame rate of 100,000 fps. The water was degassed with measured dissolved oxygen (DO) about 30%. The freestream temperature was heated from room temperature up to 90°C. The flow velocity was adjusted from 6 m/s to 8 m/s. The cavitation number σ was varied by con- trolling the tank pressure. Five different flow temperatures have been experimented in this study. The temperature data were recorded every 2 seconds, and the measurement temperature was averaged in 30 seconds of measurement. The actual freestream tem- perature measured was about 1°C around the designed temperature. The experiment conditions are shown in Table1. Table 1. Experimental conditions for NACA0015 hydrofoil in water AoA = 12 Deg. Temperature (°C) U0 (m/s) Cavitation number, σ Designed, T0 Actual 25 Not measured 60 1.60 8 70 80 Around 1°C of T0 90 Varied 7 90 1.60 6 2.2. Cavitation visualization and measurement of temperature depression Fig.2 shows the instantaneous image of the appearance of cavity with freestream temperature of (a) T0 = 25°C, (b) T0 = 60°C, and (c) T0 = 90°C on the condition of σ = 1.6, U0 = 8 m/s. Notably, the thermistor probes were not inserted in the experiment at T0 = 25°C. The shedding cavitation was visualized at T0 = 25°C. Higher temperature, the supercavitation occurred and the second thermistor probe (ThP2) was fully immersed inside the cavity. According to the visualization, the inverse thermodynamic effect was observed. Cavity became longer with the increase of freestream temperature. At high- temperature T0 = 90°C, the stronger cavitation was visualized compare to T0 = 60°C, in that the cavity length was over the observation window. Similar behavior was also reported in Cervone’s experiment [4]. Fig.3 shows the relation of measured temperature depression with freestream tem- perature on the condition of σ = 1.6, U0 = 8 m/s. The freestream temperature was varied from 60°C to 90°C. The measured result was compared with the experimental data of
5. Experimental and numerical evaluation of thermodynamic effect on NACA0015 hydrofoil cavitation in hot water 257 Yamaguchi [3]. The standard uncertainty was about 0.01°C. According to the results, the temperature depression became bigger when the freestream temperature increases. The measured temperature depression agreed with Yamaguchi’s data up to 80°C. The tempera- ture drop was measured at about 0.32°C at a freestream temperature of T0 ≈ 90°C. Al- though the cavitation appeared on the sup- porting pipe of ThP1. The appearance place was far away from the thermistor probe heat, the effect of cavitation on the measurement data is thus negligible. Fig.4 shows the measured temperature depression in the cavity regarding the cavita- tion number on the condition of U0 = 8 m/s, T0 ≈ 90°C. The temperature drop inside the cavity increased when the cavitation number getting smaller. The supercavitation was visu- alized at cavitation number σ ≤ 1.6. The non- cavitation and the developing cavitation were visualized at cavitation number σ > 2 in this study. Regarding the supercavitation region, the temperature depression increased rapidly as the cavitation number decreases. Since we Fig. 2. The visualization of cavitation aspect could not further reduce the cavitation number at: (a) T0 = 25°C, (b) T0 = 60°C, and (b) T0 = σ < 1.5, the maximum temperature depression 90°C (σ = 1.6, U0 = 8 m/s) Fig. 3. Measurement of temperature depres- Fig. 4. The influence of cavitation number on sion regarding to different freestream temper- the measurement of temperature depression ature (σ = 1.6, U0 = 8 m/s) (U0 = 8 m/s, T0 ≈ 90°C)
6. 258 Anh Dinh Le was measured at about 0.41°C in this study. For σ > 2, where the cavity did not reach the second thermistor probe ThP2, the temperature difference between the two thermistor probes was relatively small. The difference in measured results may cause by the diffu- sion effect at two thermistor probes. For 1.6 < σ < 2, the shedding cavitation, in which the ThP2 was covered by both vapor and pure water cyclically, occurred. Then, the tem- perature depression became bigger in comparison with the higher cavitation number. However, the measured temperature depression in this region was sensitive and there- fore difficult to adjust the accuracy. The instantaneous image of cavitation aspect at two different cavitation numbers (a) σ = 1.85 – the shedding cavitation and (b) σ = 1.6 – the supercavitation are shown in Fig.5. Fig.6 shows the dependence of the temperature depression regarding the freestream velocity on the flow condition of σ = 1.6, T0 ≈ 90°C. The nonlinear relationship of tem- perature depression and freestream velocity was observed. The temperature depression decreases with the increase of freestream velocity. At U0 = 6 m/s, the temperature differ- ence was measured about 0.39°C. The lower temperature depression was recorded at the freestream velocity U0 = 7 m/s, and U0 = 8 m/s. Fig. 5. Appearance of cavity in water (U0 = Fig. 6. Dependence of temperature depression 8 m/s, T0 = 90°C): (a) σ = 1.85 – the shedding regarding to freestream temperature (σ = 1.6, cavitation and (b) σ = 1.6 – the supercavitation T0 ≈ 90°C) 3. SIMULATION 3.1. Numerical method The cavitating flow was simulated using the homogeneous model approach. In that, the phases are assumed to share the same pressure, temperature, and velocity. The liq- uid phase is assumed to be a compressible fluid and the equation of state is derived from Tammann’s equation [11]. The gas phase is assumed to be an ideal gas. Therefore,
7. Experimental and numerical evaluation of thermodynamic effect on NACA0015 hydrofoil cavitation in hot water 259 the governing equations for the locally homogeneous compressible two-phase medium can be written in a simple form as for single-phase flow. In addition, a mass conser- vation equation for the gas phase is implemented that includes the phase change rate due to cavitation in the source term. The equation of state is reconstructed to close the systems [12, 13]. The standard k – ω turbulent model was used for accounting for the effect of turbulence on cavitation [14]. A cavitation model based on the Herz-Knudsen- Langumur equation [15] is used for modeling the mass transfer rate m when cavitation ∗ occurs/collapses. The influence of turbulence on the threshold vapor pressure pv(T) was calculated based on Singhal’s suggestion [16]. As in the experiment, the temperature depression increase with the increase of water temperature. To account for this phe- nomenon, a simplified thermodynamic model, which has been validated for cryogenic liquids [10], is used. The detail of the systems governing equation can be referred to the work by Anh et al. [10]. 3.2. Numerical scheme The compressible unsteady cavitating flow was simulated by an in-house code based on the finite difference method (FDM). The explicit (Total Variation Diminishing) TVD Maccormack scheme [17,18], which is a predictor-corrector type scheme, was used. Back- ward and forward discretization was used in the predictor and corrector steps, respec- tively. In the numerical simulation of cavitating flow, the strong pressure wave is gener- ated; hence, the second-order symmetric TVD scheme [18] was applied after the corrector step to ensure stability and monotonicity of the solution. The viscous terms were dis- cretized by a second-order space-centered scheme. Hence, this scheme has second-order accuracy in time and space. The scalable wall function was used [19]. This numerical scheme was validated for cavitating flow in cryogenic liquids and water at room temper- ature [9]. 3.3. Computational conditions A C-type orthogonal boundary fitted grid (253 × 70) was made over the hydrofoil as in Fig.7. In that, the inlet is located at three-chord length from the leading edge of hydrofoil; the outlet is located at five chord length from the trailing edge. At the inlet, a uniform velocity, temperature, void fraction, and turbulent quantities were specified. The Fig. 7. Computational grid for NACA0015
8. 260 Anh Dinh Le pressure regarding the experimental cavitation number was set at a reference point in the inlet boundary. The static pressure was set at the outlet 7 boundaries. No slip condition was applied at the top/bottom wall and hydrofoil. The five runs of the experiment were selected in this study as in Table2, and the numerical results were compared with the experimental data based on the visualized image and measured temperature depression. Table 2. Calculation conditions for NACA0015 hydrofoil in hot water AoA =12 deg. Designed Temperature T0 (°C) U0 (m/s) Runs σ 25 60 70 90 Run0 × Run1 × 8 1.60 Run2 × Run3 × 6 Run4 1.60 × 3.4. Results and discussion 3.4.1. Influence of freestream temperature Fig.8 shows a comparison of the time-averaged temperature depression obtained by the numerical simulation and experimental data according to freestream temperature on supercavitation condition: run1 (σ = 1.60, U0 = 8 m/s, T0 = 60.6°C), run2 (σ = 1.60, U0 = 8 m/s, T0 = 70.7°C), and run3 (σ = 1.60, U0 = 8 m/s, T0 = 91°C). The quantitatively good agreement in temperature depression was reproduced in all runs. The tendency of temperature depression agreed with experimental data, in that the degree of temperature drop in simulation was increased with the increase of freestream temperature. Fig.9 shows the comparison of numerical result and experimental data in run1 ( σ = 1.60, U0 = 8 m/s, T0 = 60.6°C) – (left) and run3 (σ = 1.60, U0 = 8 m/s, T0 = 91°C) – (right), respectively. In the figures, (a) is the instantaneous image of the cavity in the experiment, (b) is the instantaneous image of the cavity in numerical simulation, and (c) is temperature distribution. Although it is difficult to completely compare the cavity length because of the random bubble cloud at the rear of the cavity, the cavity aspect showed good agreement compare with the experiment in run1 (σ = 1.60, U0 = 8 m/s, T0 = 60.6°C). As freestream temperature shifts toward around T0 = 90°C, the supercavitation became stronger with longer cavity length in both numerical and experiment. The minimum temperature appeared at the region behind the hydrofoil trailing edge, where the vapor void fraction is high.
9. Experimental and numerical evaluation of thermodynamic effect on NACA0015 hydrofoil cavitation in hot water 261 Fig. 8. Comparison of temperature depression Fig. 9. Instantaneous distribution of cavity as- between numerical simulation and experiment pect in experiment (a), vapor void fraction in in run1 (σ = 1.60, U0 = 8 m/s, T0 = 60.6°C), run2 simulation (b), and temperature distribution (σ = 1.60, U0 = 8 m/s, T0 = 70.7°C), and run3 (c) in run1 (σ = 1.60, U0 = 8 m/s, T0 = 60.6°C) (σ = 1.60, U0 = 8 m/s, T0 = 91°C) – (left), and run3 (σ = 1.60, U0 = 8 m/s, T0 = 91°C) – (right) 3.4.2. Influence of freestream velocity Fig. 10 illustrates the comparison of the temperature depression between the present numerical solution and the experiment data at T0 = 90°C with different freestream ve- locities. The temperature depression inside the cavity is decreased when the velocity Fig. 10. Comparison of temperature depression between simulation and experiment in run3 (σ = 1.60, U0 = 8 m/s, T0 = 91°C), and run4 (σ = 1.60, U0 = 6 m/s, T0 = 90.3°C)
10. 262 Anh Dinh Le increase. The numerical results agreed with the measured data. Notably, previous stud- ies showed that the temperature depression inside the cavity is proportional to the non- dimensional thermodynamic parameter Σ∗ in Eq. (1)[20, 21]. Table3 depicts the Σ∗ with respect to the freestream velocity. It is clear that the Σ∗ becomes smaller as the velocity increases, the temperature depression is thus smaller. This behavior was consistent with the present simulation results. s ρ2 L2 C ∗ = v Σ 2 √ 3 , (1) ρl Cpl T∞ al U∞ where ρ is the fluid density and c is the chock length of the hydrofoil. In addition, Cp, αl, and L are the specific heat capacity, the thermal diffusivity, and the latent heat of the water. The subscripts v and l stand for the vapor and water phases, respectively. Table 3. Non-dimensional thermodynamic parameter for water at a different flow velocity T0 ≈ 90°C U0 (m/s) 6 7 8 Σ∗ 21.88 17.36 14.21 4. CONCLUSIONS In this paper, cavitation in hot water was studied by combined experimental and nu- merical simulation approaches. The experiment was performed in the high temperature and high-pressure water tunnel with NACA0015 as cavitator. Different flow conditions such as temperature, velocity, and cavitation number, were conducted. The temperature depression inside the cavity was measured using the high-accuracy thermistor probe. The numerical solution was conducted based on experimental data by coupling a simpli- fied thermodynamic model and governing equation. As in the experiment, the temperature depression in the cavity was increased pro- portionally with the increase of freestream temperature. The maximum temperature de- pression of about 0.41°C was measured in water at 90°C in this experiment. However, the inverse thermodynamic effect was observed, although the temperature drop was ob- served inside the cavity. The reason is still unclear. The cavitation phenomena in hot water cavitation were successfully reproduced us- ing a simplified thermodynamic model. The temperature drop and cavity volume were well predicted. The temperature depression tendency in the cavity agreed with exper- imental data under different flow conditions with a relatively small difference. Finally, it concludes that the present simplified thermodynamic model is applicable for simulat- ing the thermodynamic effect on cavitation in different liquids using the homogeneous model.
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