Melissaris 2017a - Revision history

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 The last decades there is a strong interest in predicting cavitation dynamics as it is a prerequisite in order to predict cavitation erosion. Industrial applications require accurate results in an acceptable time span and as a result there is a focus on large scale dynamics. In this paper the RANS equations are used to investigate the shedding frequency of sheet cavities in two-dimensional simulations. First a verification study is made for the NACA 0015 in 6 degrees angle of incidence. A grid sensitivity study is conducted in wetted flow and in steady (non-shedding) cavitating condition (σ=1.6). Then an investigation is conducted in order to capture the shedding frequency. The results show that only when a correction for turbulent viscosity at the cavity-water interface is used it was possible to capture the shedding frequency as found in other numerical studies. Furthermore, a validation study is conducted on a NACA66-312 α=0.8 for two different angles of attack. The obtained results are compared and validated with the experimental data from Leroux ''et al''. They indicate that the 2D shedding frequency predicted by the numerical simulations is in good agreement with the frequency obtained in the experiment.
 ==Presentation ==
 ==REFERENCES ==

@@ Line 3: / Line 3: @@
 The last decades there is a strong interest in predicting cavitation dynamics as it is a prerequisite in order to predict cavitation erosion. Industrial applications require accurate results in an acceptable time span and as a result there is a focus on large scale dynamics. In this paper the RANS equations are used to investigate the shedding frequency of sheet cavities in two-dimensional simulations. First a verification study is made for the NACA 0015 in 6 degrees angle of incidence. A grid sensitivity study is conducted in wetted flow and in steady (non-shedding) cavitating condition (σ=1.6). Then an investigation is conducted in order to capture the shedding frequency. The results show that only when a correction for turbulent viscosity at the cavity-water interface is used it was possible to capture the shedding frequency as found in other numerical studies. Furthermore, a validation study is conducted on a NACA66-312 α=0.8 for two different angles of attack. The obtained results are compared and validated with the experimental data from Leroux ''et al''. They indicate that the 2D shedding frequency predicted by the numerical simulations is in good agreement with the frequency obtained in the experiment.
 ==Presentation ==
 ==REFERENCES ==

← Older revision		Revision as of 14:39, 7 June 2017
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	The last decades there is a strong interest in predicting cavitation dynamics as it is a prerequisite in order to predict cavitation erosion. Industrial applications require accurate results in an acceptable time span and as a result there is a focus on large scale dynamics. In this paper the RANS equations are used to investigate the shedding frequency of sheet cavities in two-dimensional simulations. First a verification study is made for the NACA 0015 in 6 degrees angle of incidence. A grid sensitivity study is conducted in wetted flow and in steady (non-shedding) cavitating condition (σ=1.6). Then an investigation is conducted in order to capture the shedding frequency. The results show that only when a correction for turbulent viscosity at the cavity-water interface is used it was possible to capture the shedding frequency as found in other numerical studies. Furthermore, a validation study is conducted on a NACA66-312 α=0.8 for two different angles of attack. The obtained results are compared and validated with the experimental data from Leroux ''et al''. They indicate that the 2D shedding frequency predicted by the numerical simulations is in good agreement with the frequency obtained in the experiment.		The last decades there is a strong interest in predicting cavitation dynamics as it is a prerequisite in order to predict cavitation erosion. Industrial applications require accurate results in an acceptable time span and as a result there is a focus on large scale dynamics. In this paper the RANS equations are used to investigate the shedding frequency of sheet cavities in two-dimensional simulations. First a verification study is made for the NACA 0015 in 6 degrees angle of incidence. A grid sensitivity study is conducted in wetted flow and in steady (non-shedding) cavitating condition (σ=1.6). Then an investigation is conducted in order to capture the shedding frequency. The results show that only when a correction for turbulent viscosity at the cavity-water interface is used it was possible to capture the shedding frequency as found in other numerical studies. Furthermore, a validation study is conducted on a NACA66-312 α=0.8 for two different angles of attack. The obtained results are compared and validated with the experimental data from Leroux ''et al''. They indicate that the 2D shedding frequency predicted by the numerical simulations is in good agreement with the frequency obtained in the experiment.
		+
		+	==Presentation ==
		+

	==REFERENCES ==		==REFERENCES ==

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 |-
 |  style="vertical-align: top;"|<span style="text-align: center; font-size: 75%;">[1] </span>
-|  style="vertical-align: top;"|<span id='Bijlard'>M. Bijlard and N. Bulten, "RANS simulations of cavitating azimuthing thrusters," in ''Fourth International Symposium on Marine Propulsors'', Austin, Texas, USA, (2015). </span>
+|  style="vertical-align: top;"|<span style="text-align: center; font-size: 75%;">M. Bijlard and N. Bulten, "RANS simulations of cavitating azimuthing thrusters," in ''Fourth International Symposium on Marine Propulsors'', Austin, Texas, USA, (2015). </span>
 |  style="vertical-align: top;"|
 |-

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 The last decades there is a strong interest in predicting cavitation dynamics as it is a prerequisite in order to predict cavitation erosion. Industrial applications require accurate results in an acceptable time span and as a result there is a focus on large scale dynamics. In this paper the RANS equations are used to investigate the shedding frequency of sheet cavities in two-dimensional simulations. First a verification study is made for the NACA 0015 in 6 degrees angle of incidence. A grid sensitivity study is conducted in wetted flow and in steady (non-shedding) cavitating condition (σ=1.6). Then an investigation is conducted in order to capture the shedding frequency. The results show that only when a correction for turbulent viscosity at the cavity-water interface is used it was possible to capture the shedding frequency as found in other numerical studies. Furthermore, a validation study is conducted on a NACA66-312 α=0.8 for two different angles of attack. The obtained results are compared and validated with the experimental data from Leroux ''et al''. They indicate that the 2D shedding frequency predicted by the numerical simulations is in good agreement with the frequency obtained in the experiment.
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
-<span style="text-align: center; font-size: 75%;">VII International Conference on Computational Methods in Marine Engineering</span></div>
-−
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
-<span style="text-align: center; font-size: 75%;">MARINE 2017</span></div>
-−
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
-<span style="text-align: center; font-size: 75%;">M. Visonneau, P.  Queutey and D. Le Touzé (Eds)</span></div>
-−
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-<big>'''A NUMERICAL STUDY ON THE SHEDDING FREQUENCY OF SHEET CAVITATION '''</big></div>
-−
-−
-'''Abstract.''' The last decades there is a strong interest in predicting cavitation dynamics as it is a prerequisite in order to predict cavitation erosion. Industrial applications require accurate results in an acceptable time span and as a result there is a focus on large scale dynamics. In this paper the RANS equations are used to investigate the shedding frequency of sheet cavities in two-dimensional simulations. First a verification study is made for the NACA 0015 in 6 degrees angle of incidence. A grid sensitivity study is conducted in wetted flow and in steady (non-shedding) cavitating condition (σ=1.6). Then an investigation is conducted in order to capture the shedding frequency. The results show that only when a correction for turbulent viscosity at the cavity-water interface is used it was possible to capture the shedding frequency as found in other numerical studies. Furthermore, a validation study is conducted on a NACA66-312 α=0.8 for two different angles of attack. The obtained results are compared and validated with the experimental data from Leroux ''et al''. They indicate that the 2D shedding frequency predicted by the numerical simulations is in good agreement with the frequency obtained in the experiment.
 ==REFERENCES ==

← Older revision	Revision as of 12:38, 14 June 2017
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← Older revision		Revision as of 16:20, 6 June 2017
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	'''Abstract.''' The last decades there is a strong interest in predicting cavitation dynamics as it is a prerequisite in order to predict cavitation erosion. Industrial applications require accurate results in an acceptable time span and as a result there is a focus on large scale dynamics. In this paper the RANS equations are used to investigate the shedding frequency of sheet cavities in two-dimensional simulations. First a verification study is made for the NACA 0015 in 6 degrees angle of incidence. A grid sensitivity study is conducted in wetted flow and in steady (non-shedding) cavitating condition (σ=1.6). Then an investigation is conducted in order to capture the shedding frequency. The results show that only when a correction for turbulent viscosity at the cavity-water interface is used it was possible to capture the shedding frequency as found in other numerical studies. Furthermore, a validation study is conducted on a NACA66-312 α=0.8 for two different angles of attack. The obtained results are compared and validated with the experimental data from Leroux ''et al''. They indicate that the 2D shedding frequency predicted by the numerical simulations is in good agreement with the frequency obtained in the experiment.		'''Abstract.''' The last decades there is a strong interest in predicting cavitation dynamics as it is a prerequisite in order to predict cavitation erosion. Industrial applications require accurate results in an acceptable time span and as a result there is a focus on large scale dynamics. In this paper the RANS equations are used to investigate the shedding frequency of sheet cavities in two-dimensional simulations. First a verification study is made for the NACA 0015 in 6 degrees angle of incidence. A grid sensitivity study is conducted in wetted flow and in steady (non-shedding) cavitating condition (σ=1.6). Then an investigation is conducted in order to capture the shedding frequency. The results show that only when a correction for turbulent viscosity at the cavity-water interface is used it was possible to capture the shedding frequency as found in other numerical studies. Furthermore, a validation study is conducted on a NACA66-312 α=0.8 for two different angles of attack. The obtained results are compared and validated with the experimental data from Leroux ''et al''. They indicate that the 2D shedding frequency predicted by the numerical simulations is in good agreement with the frequency obtained in the experiment.
−
−	~~==5 CONCLUSIONS AND RECOMMENDATIONS==~~
−
−	In this study an attempt was made to verify the incompressible RANS solver in StarCCM+ in cavitating flow. Despite the three-dimensional character of cavitation dynamics a first investigation was conducted on the grid and numerical (time step, inner iterations etc.) sensitivity with the intension to predict the shedding frequency using two-dimensional domain. For the current computational set-up and the tested conditions the following conclusions are drawn:
−
−	:* When a steady sheet cavity is predicted the effect of the time step and the number of the inner iteration on the results are negligible. However, the grid density had a slight impact on the shape of the sheet cavity.
−
−	:* In the unsteady condition, on the other hand, the time step and the number of inner iterations per time step seem to play an important role on the prediction of the shedding frequency. A higher frequency was captured only when the correction for the turbulence viscosity in areas with higher vapor volume was applied. Without the correction the effect of the re-entrant jet could not be captured thoroughly, leading to a “delayed” shedding and consequently to a lower shedding frequency.
−
−	:* Furthermore, it should be noted that the number of iterations needed per time step changes for different time steps and order of temporal discretization, so it is suggested that they are selected in such a way that convergence of the total vapor volume per time step is achieved.
−
−	~~:* A grid independent solution has been reached; even the coarsest mesh was capable of capturing the dynamic shedding in a high frequency after application of Reboud’s eddy viscosity correction.~~
−
−	:* As a second step, an effort to validate the model was made comparing the numerical results with experimental data. Good agreement was obtained and the shedding frequency was accurately predicted. Discrepancies can only be observed in the maximum total volume per cycle.
−
−	~~:* Further computations on a three-dimensional domain are recommended to investigate possible alterations on the cavitation dynamics and the shedding frequency.~~
−
−	~~:* It is finally recommended to investigate the possible erosion mechanisms and the capability of predicting the potentially erosive cavitation implosions using incompressible URANS solver.~~

	==REFERENCES ==		==REFERENCES ==

← Older revision		Revision as of 16:18, 6 June 2017
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	'''Abstract.''' The last decades there is a strong interest in predicting cavitation dynamics as it is a prerequisite in order to predict cavitation erosion. Industrial applications require accurate results in an acceptable time span and as a result there is a focus on large scale dynamics. In this paper the RANS equations are used to investigate the shedding frequency of sheet cavities in two-dimensional simulations. First a verification study is made for the NACA 0015 in 6 degrees angle of incidence. A grid sensitivity study is conducted in wetted flow and in steady (non-shedding) cavitating condition (σ=1.6). Then an investigation is conducted in order to capture the shedding frequency. The results show that only when a correction for turbulent viscosity at the cavity-water interface is used it was possible to capture the shedding frequency as found in other numerical studies. Furthermore, a validation study is conducted on a NACA66-312 α=0.8 for two different angles of attack. The obtained results are compared and validated with the experimental data from Leroux ''et al''. They indicate that the 2D shedding frequency predicted by the numerical simulations is in good agreement with the frequency obtained in the experiment.		'''Abstract.''' The last decades there is a strong interest in predicting cavitation dynamics as it is a prerequisite in order to predict cavitation erosion. Industrial applications require accurate results in an acceptable time span and as a result there is a focus on large scale dynamics. In this paper the RANS equations are used to investigate the shedding frequency of sheet cavities in two-dimensional simulations. First a verification study is made for the NACA 0015 in 6 degrees angle of incidence. A grid sensitivity study is conducted in wetted flow and in steady (non-shedding) cavitating condition (σ=1.6). Then an investigation is conducted in order to capture the shedding frequency. The results show that only when a correction for turbulent viscosity at the cavity-water interface is used it was possible to capture the shedding frequency as found in other numerical studies. Furthermore, a validation study is conducted on a NACA66-312 α=0.8 for two different angles of attack. The obtained results are compared and validated with the experimental data from Leroux ''et al''. They indicate that the 2D shedding frequency predicted by the numerical simulations is in good agreement with the frequency obtained in the experiment.
−
−	~~==2 MATHEMATICAL MODELS==~~
−
−	~~===2.1 Governing equations===~~
−
−	The equations solved are the Reynolds Averaged Navier-Stokes (RANS) equations, where each instantaneous quantity can be split into time-averaged and fluctuating components. An incompressible segregated flow model is selected solving the integral conservation equations of mass and momentum in a sequential manner combined with the SIMPLE pressure-velocity coupling algorithm. From the basic principles of conservation of mass and momentum, the governing equations are written as follows:
−
−	~~{\| style="width: 100%;"~~
−	\|-
−	\|
−	~~\| <math>\frac{\partial \rho }{\partial t}+\nabla \cdot \left( \rho \mathit{\boldsymbol{u}}\right) =</math><math>0</math>~~
−	~~\| (1)~~
−	\|-
−	\|
−	~~\| <math>\frac{\partial }{\partial t}\left( \rho \mathit{\boldsymbol{u}}\right) +\nabla \cdot \left( \mathit{\boldsymbol{\rho uu}}\right) =</math><math>-\nabla p+\rho f+\nabla \cdot \tau</math>~~
−	~~\| (2)~~
−	\|}
−
−	<span id='_Toc463969601'></span>where '''u''' is the velocity tensor, ρ is the fluid density, <math display="inline">\, \nabla p</math> the pressure gradient,'' '' <math display="inline">\rho f</math> the exterior force density per unit mass and τ the viscous part of the stress tensor.
−
−	The multiphase model used is the Volume of Fluid (VOF) method. Within the VOF approach, the fluid is treated as a single continuum, assuming a no-slip condition between liquid and vapor phases, with varying properties in space according to its composition <math display="inline">{\, a}_{v}</math>. The volume fraction of the components is determined from the condition:
−
−	~~{\| style="width: 100%;"~~
−	\|-
−	\|
−	~~\| style="text-align: center;"\| <math>{a}_{v}+{a}_{l}=1</math>~~
−	~~\| style="text-align: right;"\|(3)~~
−	\|}
−
−	~~while density and viscosity are defined as:~~
−
−	~~{\| style="width: 100%;"~~
−	\|-
−	\|
−	~~\| <math>\rho ={a}_{l}{\rho }_{l}+{\alpha }_{v}{\rho }_{v}\quad \, \, and\quad \, \mu ={a}_{l}{\mu }_{l}+</math><math>{a}_{v}{\mu }_{v}</math>~~
−	~~\| style="text-align: right;"\|(4)~~
−	\|}
−
−	~~===2.2 Turbulence modeling===~~
−
−	In this study the SST k-ω turbulence model developed by Menter [5] is used in order to fully resolve the boundary layer. This approach effectively blends a k-ε model in the far field with a k-ω model near the wall. Reboud and Delannoy [6] showed the important role of the re-entrant jet on the cavity break-off cycle. However, the use of this turbulence model leads to very strong turbulent viscosity in the cavity wake hindering the re-entrant jet formation. It is stated by Reboud ''et al''. [7] that this effect, which is not representative of the real behaviour, has been analysed to be related to the hypothesis of homogeneous flow and its no-slip condition between the two phases. That no-slip condition behaves as an artificial increase of dissipation.
−
−	~~That problem has been treated by an empirical reduction of turbulence dissipative terms in the two-phase regions, by modifying the turbulent viscosity [7]:~~
−
−	~~{\| style="width: 100%;"~~
−	\|-
−	\|
−	\| <math>{\mu }_{t}=f\left( \rho \right) {C}_{\omega }\frac{k}{\omega };\quad f\left( \rho \right) =</math><math>{\rho }_{\nu }+\frac{{\left( {\rho }_{m}-{\rho }_{\nu }\right) }^{n}}{{\left( {\rho }_{l}-{\rho }_{\nu }\right) }^{n-1}};\quad \, n\gg 1</math>
−	~~\| style="text-align: right;"\|(5)~~
−	\|}
−
−	where <math display="inline">{\rho }_{\nu }</math> is the vapor density, <math display="inline">{\rho }_{l}</math> the liquid density and <math display="inline">{\rho }_{m}</math> the mixture density. For the constant <math display="inline">n</math> a recommended value <math display="inline">n=</math><math>10</math> has been used. This modification improves the numerical simulations by taking into account the influence of the local compressibility effects of the vapor/liquid mixture on the turbulent structure.
−
−	~~===2.3 Cavitation modeling===~~
−
−	~~The conservation equation that describes the transport of vapour is similar to the mass conservation for liquid and is described by:~~
−
−	~~{\| style="width: 100%;"~~
−	\|-
−	\|
−	~~\| <math>\frac{\partial {a}_{v}}{\partial t}+\nabla \cdot \left( {a}_{v}\mathit{\boldsymbol{u}}\right) =</math><math>{S}_{{a}_{v}}</math>~~
−	~~\| style="text-align: right;"\|(6)~~
−	\|}
−
−	In equation (6), <math display="inline">{S}_{{a}_{v}}</math> represents the source of volume fraction of vapor. In order to close the system of equations formed by the RANS equations and the transport equation for the vapor, a cavitation model should be introduced for the source term of the volume fraction of vapor. The cavitation model used is the model proposed by Schnerr-Sauer (2000) based on a simplified Rayleigh-Plesset equation, which neglects the influence of bubble growth acceleration, as well as viscous and surface tension effects:
−
−	~~{\| style="width: 100%;"~~
−	\|-
−	\|
−	~~\| <math>\frac{dR}{dt}=sign\left( {p}_{\nu }-p\right) \sqrt{\frac{2\left\| {p}_{\nu }-p\right\| }{3{\rho }_{l}}}</math>~~
−	~~\| style="text-align: right;"\|(7)~~
−	\|}
−
−	Where <math display="inline">{p}_{\nu }</math> is the saturation pressure, <math display="inline">p</math> is the local pressure around the bubble and <math display="inline">{\rho }_{l}</math> is the fluid density. According to this rate the source term in equation (6) is defined as:
−
−	~~{\| style="width: 100%;"~~
−	\|-
−	\|
−	~~\| <math>{S}_{{a}_{v}}=\frac{4\pi {R}^{2}{n}_{0}}{1+\left( \frac{4}{3}\pi {R}^{3}\right) {n}_{0}}\frac{dR}{dt}\,</math>~~
−	~~\| style="text-align: right;"\|(8)~~
−	\|}

	==3 CASE DESCRIPTION==		==3 CASE DESCRIPTION==