DES Simulation of Flow Field of Propeller Tip Vortex

SHI Li-pan,XIONG Ying,SUN Hai-tao

(1 Dept.of Naval Architecture,Naval University of Engineering,Wuhan 430033,China;2 College of Basic Education for Commanding Officers,National University of Defense Technology,Changsha 410072,China)

0 Introduction

The tip vortex is a complicated three-dimensional viscous flow phenomenon which will be formed if the propeller is rotating in the flow field.With the velocity of flow field in the vicinity of the tip vortex core region increasing,the pressure of the core decreases significantly.The tip vortex cavitation will occur in the center of the vortex,if the pressure drops below the saturated vapor pressure.Tip vortex cavitation is of major concern in the design stage of propellers since it is an important source of noise.In order to avoid or control the tip vortex cavitation,flow field of the propeller needs to be simulated by numerical method.So it is very important and significant to study the state of the propeller blade wake flow field.

The experimental investigation of the propeller wake plays an important role in the performance analysis of ship propulsion.The characters of the tip vortex and wake structure are measured by using advanced flow visualization and non-intrusive measurement techniques traditionally.As the Laser Doppler Velocimetry has great advantages of velocity direction recognition and good frequency response of a non-intrusive probe,it is widely used in the measurements of the propeller wake flow.Min[1]and Hsiao[2]studied the tip vortex evolution by using the LDV.Jessup[3-4]and Dong[5]carried out extensive experiments for the DTRC 4119 using a LDV system in a water tunnel and substantial measured data on the flow field in the wake.Comparison of the experimental data between the LDV and PIV was made by Li[6-7].These data were all used to compare with the numerical results.

Numerical computations based on the Navier-Stockes equation have been used to predict the detail flow structure of the propeller flow field.Tang and Dong[8]made a simulation of the flow field around the propeller by using RANS method combined with the non-staggered grid system.Their study shows that the method used to predict the viscous flow around the propeller not only qualitatively but also quantitatively.Stanier[9]investigated the blade wake flow feature of the DTRC 4119 by RANS method.The open water performance and the predicted velocities show good agreement with the measurements,but significant scale effect had been detected between the model and full scale propellers.Turnock[10]enhanced an existing 2D vortex identification algorithm to track the helical path of the tip vortex generated by a marine propeller DTRC4119.With a suitably mesh concentrated about the tip vortex core,significant improvements had been demonstrated to predict the vortex tracking.Bulten[11]found that the choice of RANS turbulence model extended a limited effect on the computation results.But local mesh refinement method enables a deep analysis of the flow phenomena in the tip vortex.LES with a rotating mesh has been applied for the simulation of the flow around a propeller.Compared the calculated data with extensive PIV and LDV measurements,Bensow[12]found that the numerical results without the refined mesh had deteriorated significantly at approximately one propeller diameter downstream of the propeller.Roberto Muscari[13]overcame the over predicted eddy of the simulation and made a success to capture the flow detail of propeller E779A accurately.

To save the computational resource and precisely capture the tip vortex structure,the DES method is employed in the simulation of the flow field around the DTRC 4119.Present result demonstrates the capability of the DES method to handle the propeller flows through the comparison between calculation results and experimental data.

1 Numerical model

1.1 Turbulence modeling

The propeller blade wake flow is one of the most complicated flow field in naval hydrodynamic.The blade inflow varies significantly as the propeller rotates.It contains the intense vortex sheet which travels downstream and exerts great effect on the wake flow.In this paper,the DES based on the SA model is adopted to the simulation to improve the precision and reduce the resource of the computation.DES method is the mixer of the LES and the RANS.For the flow close to the wall,the RANS model is used.The LES model is employed for the flow away from the wall.

The governing equation here can be written as below:

The DES based on the SA model is adopted.As a one-equation turbulence model,the SA model can solve a transport equation of turbulent eddy viscosity.The switch between RANS and LES in the original DES-SA model is achieved by replacing the explicit length scale.

In formula(5),dRANSrepresents the wall distancelength scale of the grid size,in which Δx,Δy,Δz represent the grid size in three direction respectively,the model constant CDES=0.65.

1.2 Geometry and computation grid

The simulation was performed for David Taylor propeller 4119,which is a three-blade propeller with 12 inch diameter.Since the hub and the blade root are complicated,some geometry simplifications are made for the numerical study.The root fillets and a root trailing edge cut-out are ignored.In order to improve the quality of the grids,propeller blades are assumed to be mounted on an infinite constant-radius hub/shaft cylinder.The computational domain is established and is shown in Fig.1,in which the inlet boundary is located 4 propeller radius upstream and the outlet boundary is 10 radius downstream of the propeller disk plane.The radius of the computational domain is chosen as 4 times greater than the propeller radius.

Fig.1 The computation domain

To create an appropriate structure grid inside the domain,the combination of H-type grid and O-type grid block structure is applied.Finally,the grid with a total of 5.4 million cells is created for the current domain.The first grid spacing is specified as 2.5×10-5of the diameter of the propeller on the blade surface.In that case,the y+is between 1 and 10 in the first grid on all blade surfaces.As the velocity gradient of the vortex core is great,to minimum discrete er-ror of the mesh,at least 15 points are used in the across direction of the vortex core.

1.3 Boundary conditions

All the boundary conditions are specified in an implicit manner.The boundary conditions are as follows:velocity boundary is used both at the inlet and the outer radial surfaces;the noslip condition is applied on the blade and shaft/hub surface;static pressure outlet is adopted.The turbulence intensity is chosen as 5%and eddy viscosity ratio is 10 at the inlet.

In the present study,the numerical computations are carried out at five different advance coefficients J=U0/nD=0.5,0.7,0.833,0.9,1.1,here U0is the axial velocity,n is the propeller rotating speed and D is the propeller diameter.J=0.833 is the design condition.The advance ratios above correspond to different Reynold numbers,which are from 1.37×106to 1.43×106,the Reynold numbers are based on the propeller blade chord length at 0.7R section and the vector sum velocity of the inflow velocity and the rotational component.

2 Numerical simulation

Before the analysis the detailed flow around the propeller,the numerical method should be validated firstly.The numerical results here are systematic compared with the experimental data measured by Jessup(1989)[3]to validate current numerical method.

2.1 Validation of the open water performance

Validation of the open water performance is one of the most important things in the simulation of the flow around the propeller.The first step is comparison of the non-dimension parameters with the experimental data.

The non-dimension parameters of propeller are described as:

Fig.2 The open water performance of the propeller

where T is the thrust of the propeller,QPis the torque of the propeller,ρ is the fluid density,n is the propeller rotational speed,D is the diameter of propeller,J is the advance ratios,Ktis the thrust coefficient and Kqis the torque coefficient of the propeller,respectively.

From the comparison in Fig.2,it is seen that the DES method predicts the measured results fairly well for all advance ratios,especially at the designing point of the propeller.The error is less than 4%compared with the experimental results,which means that this method is reliable to predict the open water performance of propeller.

2.2 Analysis of the blade surface pressure distribution

The measurement of the pressure distribution is accomplished by Jessup using LDV method.Figs.3-5 illustrate the pressure distributions of Propeller DTRC4119 at the 0.3,0.7 and 0.9 radius respectively.

Fig.3 The pressure distribution at r/R=0.3

Fig.4 The pressure distribution at r/R=0.7

The pressure coefficient is defined by the 22nd International Towing Tank Conference Propulsion Committee.

In which Vx=U0,p is the pressure on the blade section,p0is the reference pressure,n is the rotating speed of the propeller.

The DES methods predict the measured results fairly well in general.All the numerical datashows a very good agreement with the experimental data over most of the chord.However the numerical result has a sight difference in the measurement results near the leading edge.The greatest discrepancy between predictions and measurement occurs at the 0.3 radius,which may be due to model geometry simplification of the hub.

2.3 Analysis of the flow field of the propeller

The accurate prediction of the flow field around the propeller is the basis for the simulation of the tip vortex cavitation and is useful to get the coherent of the tip vortex and its development.

Based on the detail flow field near the tip of propeller,the velocity and pressure distribution can be simulated exactly.And the flow field plays an important role in the prediction of the propeller exciting force.Results of the axial velocity distribution downstream of propeller are shown in Fig.6.The measurement planes are located at a distance between r/R=0.25 and r/R=1.0 with an increase of 0.125r/R.In the x direction,the axial velocity decreases as the flow travel downstream.The phase of the axial velocity varies with the propeller if the wake travel downstream,and the amplitude decrease if travel downstream.

Fig.6 Variation of axial velocity downstream of the propeller

Fig.5 The pressure distribution at r/R=0.9

Fig.7 is the results of the velocity distribution downstream of the propeller.The measurement plane is located at a distance of 0.328R downstream of the propeller disc plane.The data shown in Fig.7 is measured at the radius of r/R=0.7.The velocity in the axial direction is over predicted by the CFD calculations,but the error is reasonable.Meanwhile,agreement between the measurement and the calculation is satisfactory.

In order to do further research detail for the flow field,the counters of axial velocity at the plane of x/R=0.328 are illustrated in Fig.8.Agreement between the measurements and calculations is quite good for all radius except those near the hub,which is due to the geometrized simplification of the hub and cap by a cylinder.The accuracy of the prediction of the flow field in the vortex core so far is in good agreement with the measurements.

Fig.7 Comparison of measured and calculated velocity field components downstream of the propeller for radius r/R=0.7,x/R=0.328

Fig.8 The counters of the axial velocity at the plane of x/R=0.328

2.4 Analysis of the propeller tip vortex

In the simulation process,it is very important to identify the shape and the location of the tip vortex of propeller.Here,the positive second invariant‘Q’is introduced to define the propeller tip vortex.The definition of Q can be written as below.

in which,S and Ω are the symmetric and anti-symmetric components of the ▽u respectively.

In present paper,the Iso-surface of the‘Q’represents the tip vortex of the propeller shown as Fig.9,in which the counter of the pressure was identified on the tip vortex surface.Compared with the RANS method,the DES result indicates that the present tip vortex can keep its strength and travel downstream for a long distance.That is to mean that the DES method can avoid the over-predicting of eddy viscosity along the vortex core,which is suitable for predicting the downstream-field structure of the propeller.

Fig.9 Iso-surface plot of constant vorticity

In the simulation of tip vortex,the location of vortex core is one of the most important factors.Fig.10 illustrates the location of the tip vortex core with the experimental and simulated results in the radial direction.It is easy to conclude that present numerical result fits well with the experimental data in the condition x/R≤0.1.For the downstream of the tip vortex,the radius of the numerical result is a little greater than the experimental data.Such difference may be induced by the ignoring hub effects.In general,the discrepancy of the vortex core location in the radial direction is less than 3%compared with the experimental and simulated results,which shows the great application prospect of DES in the prediction problem of tip vortex location.

Fig.10 Radial location of tip vortex

3 Conclusions

Based on the Detached Eddy Simulation method(DES),the flow field around the propeller numbered as DTRC 4119 was simulated numerically and the hydrodynamic performance of this propeller is summarized.Compared with the experimental results,some numerical conclusions can be drawn as follows.

(1)In order to reduce the discrete error induced by the grid,the mesh refinement was adopted in the process of performance simulation for the tip vortex core by DES,which contributes to avoid the over-predicting of the eddy viscosity along the vortex core and to keep the tip vortex travel downstream longer with the stable strength.Additionally,this numerical method can locate the vortex core location with fewer grids exactly.In the radial direction,the error of the vortex core’s location is less than 3%compared to the experimental results.Present method is applicable to predict the formation and location of the tip vortex.

(2)The calculation results indicate that DES numerical method can exactly predict the velocity distribution in tip vortex flow field.However,the pressure distribution in the inner radius is greater than the experimental results.Such discrepancy may be related to the simplification of the hub model.

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