Design and Output Performance Model of

energies Article

Design and Output Performance Model of Turbodrill Blade Used in a Slim Borehole Yu Wang 1 , Bairu Xia 1, *, Zhiqiao Wang 1, *, Liguang Wang 1,2 and Qin Zhou 1 1 2

*

School of Engineering and Technology, China University of Geosciences, Beijing 100083, China; [email protected] (Y.W.); [email protected] (L.W.); [email protected] (Q.Z.) China Railway Rolling stock Corporation (CRRC), Beijing Locomotive Co., Ltd., Beijing 100072, China Correspondence: [email protected] (B.X.); [email protected] (Z.W.); Tel.: +86-10-82321954 (Z.W.); Fax: +86-10-8232-8581 (Z.W.)

Academic Editor: Kamel Hooman Received: 1 September 2016; Accepted: 30 November 2016; Published: 8 December 2016

Abstract: Small-diameter turbodrills have great potential for use in slim boreholes because of their lower cost and higher efficiency when used in geothermal energy and other underground resource applications. Multistage hydraulic components consisting of stators and rotors are key aspects of turbodrills. This study aimed to develop a suitable blade that can be used under high temperature in granite formations. First, prediction models for single- and multi-stage blades were established based on Bernoulli’s Equation. The design requirement of the blade for high-temperature geothermal drilling in granite was proposed. A Φ89 blade was developed based on the dimensionless parameter method and Bezier curve; the parameters of the blade, including its radial size, symotric parameters, and blade profiles, were input into ANASYS and CFX to establish a calculation model of the single-stage blade. The optimization of the blade structure of the small-diameter turbodrill enabled a multistage turbodrill model to be established and the turbodrill’s overall output performance to be predicted. The results demonstrate that the design can meet the turbodrill’s performance requirements and that the multistage model can effectively improve the accuracy of the prediction. Keywords: slim borehole; granite section; turbodrill; multistage simulation models; output performances prediction

1. Introduction High dry rock (HDR) [1] can be directly extracted to obtain hot steam and water that can be used to generate clean energy [2]. Tibet, Yunnan, Hainan, and the northeast and southeast coastal areas of China have a large amount of hot dry rock geothermal resources. Because small-diameter drilling can greatly reduce the labor intensity and cost of extracting such resources, such drilling can be regarded as a potential method for use in geothermal exploration [3]. HDR primarily consists of igneous or metamorphic rocks of high hardness and poor drillability, such as granite and gneiss; the temperature of a high-temperature geothermal reservoir is typically greater than 200 ◦ C and can even reach 500 ◦ C. When drilling a slim hole using a conventional drill, the amount of borehole friction is excessively high, thus making it difficult to pass the power to the bottom [4]. The common screw drill cannot be used under conditions of high temperature [5] with large rotational vibration. Practical work shows that an all-metal turbine drill with impregnated diamond bits [6] has good temperature adaptability and high efficiency in terms of the hard rock formations [7]. The first application of turbodrills and hybrid bits for drilling cretaceous formations with high chert content was reported in the south Mexico region [8]. A turbine is made of several stages. Each stage is made of one or several rows of blade rings [9], which determine the output characteristics of the turbo-drill [10]. The key to success is to match the output characteristics with the formation properties. Therefore, the turbine drill design must first be

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based on the formation properties based on the appropriate performance indicators that are used to conduct the individual design of the blades. The accuracy of the blade’s design is critical to the success of the turbodrill [11]. Before the manufacture of the turbine blades and its mold, it is particularly important to accurately predict its output performance, which in turn guides the optimization design of the turbine blades. Many achievements have been made during the century of development of turbodrill technology [12]. Before 2000, the conventional turbine drill size was generally greater than 5”. With the increased implementation of coiled tubing technology [13], the use of small-diameter turbine drills has become a topic of increasing interest after slowly transitioning from use in oil drilling to areas of high-temperature geothermal drilling, among other applications. However, regardless of the specifications of the turbine drill, the blade design and field research have become the main aspects of research on small-diameter turbodrilling. Jin and Daliang [14] analyzed the influence of the blade profile on the flow parameters of liquid flow and found that the turbine performance is mainly affected by the uncontinuous curvature on the blade profile. Reference [15] detailed the design enhancements made to the turbodrill to establish a shorter tool with more power to address current and future applications. Reference [16] analyzed the applications and developments in turbodrills based on an analysis of recent runs on Coiled Tubing (CT). Ding et al. [17] applied CFX-BladeGen to develop the single-turbine-blade model and performed a numerical simulation calculation for a Φ115 mm turbodrill. Hu et al. [18] analyzed the principle and characteristics of the Bezier curve used in the design of a turbine blade. Reference [19] examined the history of turbodrilling and described a number of the harshest and most complex drilling environments in which turbodrills have been notably successful. Reference [20] described several improvements to the turbodrill design (such as blade design) that have enabled reductions in the tool length, thereby allowing easier rig up for coiled tubing applications. Mokaramian et al. [21] conducted computational fluid dynamics (CFD) simulations to determine the performance of a single-stage turbodrill with different rotation speeds and mass flow rates. The optimum design parameters for achieving the required rotation speed and torque for hard-rock drilling were proposed. In Reference [22], after using Solidworks software to draw the turbine blade profile, Fluentsoftware was used to simulate and analyze the flow field pressure and velocity change of the turbine cascade of the commonly used five-circarc profile and cubic polynomial profile. Hongbo et al. [23] designed a turbodrill blade according to the quintic polynomial and used the Solidworks 3D modeling software and a single-blade model to analyze the hydraulic performances of the turbine blades under different viscosity levels. Zhitao et al. [24] built a single-stage turbodrill model based on CFD software to simulate blade performance at different rotation speeds. Yu et al. [25] built a computational model of a single-stage blade on ANSYS CFD for a Φ127 turbodrill applied in a crystallized section under high-temperature and high-pressure conditions. Miyazaki et al. [26] developed a turbine-driven coring system for use in hard rock. The turbine blade used was the type that provides high-rotation speed without a Leaf crown, and it has been tested on shore. The Φ127 turbine blade was established based on the Bezier curve, experimental design theory, and the response surface method. A single-stage blade simulation model was built to study the performance of the blade [27]. Qiang et al. [28] constructed multiple-sectional linear turbine blades according to five polynomial methods. A single-stage turbine runner mesh model was built to simulate the increase in hydraulic efficiency. In summary, the current drill turbine blade design is mainly based on the principle of an axial turbine, i.e., the conservation of energy and momentum of the fluid momentum theorem. However, the current design mainly focuses on studying individual single-stage turbine blades. As a result, there are three main aspects to be improved in the design: (1) the drilling mud flow is ignored when using the energy conservation in studying a single-stage blade, without considering the centrifugal field; (2) the interaction between the blades at the same level is ignored when using a variety of curves to design the turbine blades to predict the performance; and (3) it is generally assumed that the energy of each stage is the same regarding the overall performance of the turbine drill, with the predicted

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performance often often based based simply simply on on the the product product of of aa single-stage single-stage turbine turbine performance performance and and the the stage stage performance under consideration. In fact, each stage of the single-stage blade has a corresponding energy loss, under consideration. In fact, each stage of the single-stage blade has a corresponding energy loss, causing the the output output energy energy to to not not be be equal equal to to the the overall overall energy energy input. input. Based Based on on the the aforementioned aforementioned causing assumptions, the boundary conditional difference for a small-diameter turbine drill is greater assumptions, the boundary conditional difference for a small-diameter turbine drill is greater than than that thatthe forlarge-diameter the large-diameter turbine because the small size its radial pressure for turbine drill drill because of theofsmall size of itsofradial and and axialaxial pressure drop.drop. This study study aimed aimed to to design design turbine turbine blades blades to to be be used used under under high-temperature high-temperature conditions conditions and and in in This hard rock formations. First, prediction models of a single-stage turbine blade and a multi-stage turbine hard rock formations. First, prediction models of a single-stage turbine blade and a multi-stage turbine blade were were developed developed based based on on the the modified modified Bernoulli Bernoulli Equation Equation to toovercome overcome the theabove-described above-described blade drawbacks, thereby improving the accuracy of the final results. The specifications of the blade blade were were drawbacks, thereby improving the accuracy of the final results. The specifications of the raised based on the hard-rock formation properties of the high-temperature geothermal reservoir. raised based on the hard-rock formation properties of the high-temperature geothermal reservoir. The geometrical geometrical parameters parameters and and blade blade profile profile of of aa Φ89 Φ89 mm mm blade blade were were developed developed according according to to the the The dimensionless coefficient method and Bezier curve design theory; three-dimensional solid modeling dimensionless coefficient method and Bezier curve design theory; three-dimensional solid modeling of of the turbine blades was performed, and the modeling results were imported into the the turbine blades was performed, and then, thethen, modeling results were imported into the ANSYS/CFX ANSYS/CFX module to obtain a single-stage multi-leaf computational runner, thus completing the module to obtain a single-stage multi-leaf computational runner, thus completing the optimization optimization of the small-diameter turbine blade structure. Finally, a multi-stage turbine simulation of the small-diameter turbine blade structure. Finally, a multi-stage turbine simulation model was model wasto developed tooverall predictoutput the overall output performance ofdrill. the turbine drill. developed predict the performance of the turbine 2. Hydrodynamic Hydrodynamic Model Model of of aa Turbodrill TurbodrillBlade Blade 2. 2.1. 2.1. Hypothesis of of the the Model Model The The turbodrill turbodrill blade blade is is made made of of aa stator stator and and rotor, rotor, both both of of which which are are axial-flow axial-flow hydraulic hydraulic components. Figure 1 shows a single-stage blade; its stator can be tightened by an axial force. Through components. Figure 1 shows a single-stage blade; its stator can be tightened by an axial force. stator blade 1, the drilling mud can flow rotor twoblade different movements Through stator blade 1, the drilling mudand canthen flowpass andinto then passblade into 2; rotor 2; two different occur duringoccur this process: circular and circular relative and movement. shaft 3 and the stator can movements during this process: relative Rotation movement. Rotation shaft 3 and theoutput stator the hightorque speed. at Anhigh overall turbine formed through a series of connections between cantorque outputat the speed. Ansection overallis turbine section is formed through a series of the multi-stage turbodrill blades. connections between the multi-stage turbodrill blades. Drilling fuild

2 1

3

R2 R R1

Figure 1. 1. Schematic Schematic of of the the turbodrill turbodrill blade blade assembly. assembly. 11 stator stator blade; blade; 22 rotor rotor blade; blade; 33 rotation rotationshaft. shaft. Figure

As shown in Figure1, the fluid into the turbine will flow between the surfaces of the two As shown in Figure 1, the fluid into the turbine will flow between the surfaces of the two cylinders cylinders with R1 and R2. However, each fluid mass point has one distance to the axial line, resulting with R1 and R2 . However, each fluid mass point has one distance to the axial line, resulting in different in different interactions between the blades and the relative velocity of the fluid. Therefore, there is interactions between the blades and the relative velocity of the fluid. Therefore, there is one structural one structural characteristic cylindrical surface with diameter R among the cylinders, whose velocity characteristic cylindrical surface with diameter R among the cylinders, whose velocity is assumed to is assumed to be the mean of the overall system. The energy accumulated by motion at this velocity be the mean of the overall system. The energy accumulated by motion at this velocity can represent can represent the overall rotational kinetic energy. Based on the element theory method (ETM), the the overall rotational kinetic energy. Based on the element theory method (ETM), the mean diameter is mean diameter is given by: given by: 22 RR3113−−RR3223 R = (1) R = 3 R22− R22 (1) 3 R1 − R2 1

2

The model is established based on the Euler equation and the following assumptions: (1) the fluid The model is established based on the Euler equation and the following assumptions: (1) the is a Newtonian fluid; (2) the blade is infinitely thin; and (3) no flow loss and fluid compression loss out fluid is a Newtonian fluid; (2) the blade is infinitely thin; and (3) no flow loss and fluid compression

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loss out of the stator cylinder occur. Based on these assumptions, the drilling fluid can flow in accordance the occur. blade’sBased requirements without friction of the stator with cylinder on these assumptions, theloss. drilling fluid can flow in accordance with the blade’s requirements without friction loss. 2.2. Inertial Force Field 2.2. Inertial Force Field The kinetic energy and pressure energy of the drilling fluid will be transformed and The kineticinto energy and pressure energy of theoperation drilling fluid will bethe transformed redistributed redistributed mechanical energy during through turbodrilland blade, thereby into mechanical energy during operation through the turbodrill blade, thereby producing the[25], output producing the output driven energy of the rotation shaft. In the results of previous studies the driven energy of the rotation In the resultsisofignored; previoushowever, studies [25], the influence of the rotor due influence of the rotor due toshaft. rotation motion in practice, the drilling fluid is to rotation motion is ignored; however, in practice, the drilling fluid is influenced by not only gravity influenced by not only gravity but also the centrifugal force, as shown in Figure 2. The three but also the centrifugal as shown 2. The three analysis dimensional coordinate system is built dimensional coordinateforce, system is built in toFigure describe the force of the drilling mud, shown as to describe the force analysis the drilling mud,ofshown as Figure 2. Accordingforce to the state Figure 2. According to the of actual flow state drilling fluid, centrifugal is actual in theflow plane of of drilling fluid, centrifugal force is in the plane of coordinates XOY, and the direction of the gravity is coordinates XOY, and the direction of the gravity is the same as the direction of the coordinate Z. As the same the as the direction coordinateforce Z. As a result, energyinfrom the centrifugal force a result, energy from of thethe centrifugal should be the included Bernoulli's Equation. Theshould actual be included in Bernoullis Equation. The actual inertial force field is shown in Figure 2. inertial force field is shown in Figure 2.

y

ω2y ω2r

A z 0

ω2x

R2

x R1

ω Figure 2. 2. Inertial force force field field of of the the turbodrill turbodrill blade. blade. Figure

Here, we we assume assume that that the the turbodrill turbodrill blade blade will will maintain maintain aa stable stable rotation rotation speed speed during during drilling drilling Here, operation. The rotating turbodrill blade is chosen as the reference system, in which the drilling fluid operation. The rotating turbodrill blade is chosen as the reference system, in which the drilling fluid is is relatively constant. Select point A on one streamline of the drilling mud with diameter r, on which relatively constant. Select point A on one streamline of the drilling mud with diameter r, on which the gravity and inertial centrifugal force are exerted. Its components along the x-, y-, and z-axes are, the gravity and inertial centrifugal force are exerted. Its components along the x-, y-, and z-axes respectively: are, respectively:  2   X X == ω ω22xx (2) Y = ω y  YZ ==ω−2gy (2)



Z = −g Accordingly, the definition of potential  function produced by mass can be expressed by the formula: Z Z 1 by mass can be expressed by the Accordingly, the definition of potential function produced W = dw = Xdx + Ydy + Zdz = ω 2 r2 − gz (3) 2 formula: Combining the potential function produced by mass shown in Equation (3) and the Bernoulli 1 2 2 W = dw =theXdx Zdz = for r −unit gz weight of drilling mud(3)is + Ydy +equation ω the equation, in the rotating environment, Bernoulli 2 expressed as: 2 r2 p u2 by ωmass Combining the potential function in Equation (3) and the Bernoulli z +produced + − =shown C (4) 2g 2g equation, in the rotating environment, theρgBernoulli equation for the unit weight of drilling mud is expressed as:





z+

p u2 ω 2r 2 + − =C ρ g 2g 2g

(4)

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2.3. 2.3. Energy Transformation TransformationModel Model To To better better illustrate illustrate the the three-dimensional three-dimensional fluid flow, flow, the the structural structural characteristic characteristic surface surface of the the drilling drilling mud is is expanded expanded into into aa 2-dimensional 2-dimensional map. As shown in Figure 3, the the cross-line cross-line of of the the stator stator and and rotor rotor represents represents the the section section of of aa certain certain position position of of the the blade. blade. The flow routine routine can can be be divided divided into into two two parts: parts: one is from stator stator entrance 0-0 to stator exit 1-1 (which is used to guide the drilling fluid), and entrance 1-1 1-1 to to rotor rotorexit exit2-2 2-2(which (whichisisused usedtotodrive drivethe therotation rotationshaft). shaft). and the other is from rotor entrance

0

0

1

1

2

2

Figure Figure 3. 3. Drilling mud flow flow in in aa turbodrill turbodrill blade. blade.

For the the first-stage first-stage stator, stator, the the pressure pressure energy energy of of the the fluid fluid will will be be transformed transformed into into kinetic kinetic energy energy For and partial partial hydraulic mechanical energy output. There is a is hydraulic loss and hydraulic loss lossbecause becauseofofthe thelack lackofof mechanical energy output. There a hydraulic during this process.According to Bernoulli's equation, the energy at the input and output of the loss during this process.According to Bernoulli’s equation, the energy at the input and output of the turbodrill stator stator is is given given by: by: turbodrill  c202 p0  + 2g + z0 E0 = ρg   p c  0 0  E =  0 ρp g + 2c2g + z0 (5) E1 = ρg1 + 2g1 + z1   2   p c  = E11 + + h1hs1+ z1 (5) EE01 = g ρ 2g  For the first-stage rotor, the majorityof will be transformed into mechanical energy = Eenergy E0the 1 + hhs1  rotation energy output. The flow of drilling fuild is not and hydraulic loss because of the mechanical  only affected by gravity, but also by the centrifugal force. According to Bernoulli’s equation, the energy at theFor input output rotor, of the the turbodrill rotor is given by:will be transformed into mechanical energy theand first-stage majority of the energy and hydraulic loss because of the mechanical rotation energy output. The flow of drilling fuild is not  c21 p1 E = + + zforce.  only affected by gravity, but also  by the centrifugal According to Bernoulli’s equation, the 1 1  ρg 2g  2 energy at the input and output of the turbodrill rotor is given by: 2 2 c p (6) E2 = ρg2 + 2g2 + z2 − ω2gR    2  E = Ep1 + hc1 + z1  E11 = ρ g2 + 2 hr1 g  According to the Equations (5) and (6), the pressure energy  ω 2 R 2 of the stator and rotor and the overall p2 c22 = + + − E z (6)  2 2 loss of the first-stage stator and rotor can be written 2g ρ g 2 g as follows:    E = E + hhr1 ∆ps1 p0 − p1  1c21 −c202   =  ρg ρg = 2g + ( z1 − z0 ) + h hs1    2 2 c2 − c2 ∆pr1 p1 − p2 (7) = = 22g 1 + (z2 − z1 ) + hhr1 − ω2gR ρg ρg  According to the Equations (5) and (6), the pressure energy of the stator and rotor and the overall  2 2  ∆ps1 c2 − c0 ω 2 R2  r1 loss of the first-stage stator and ∆p rotor can be written as follows: ρg + ρg = 2g + ( z2 − z0 ) + ( h hs1 + h hr1 ) − 2g  Δps1 p0 − p1 c12 − c02 Although the flow of each is +of( zthe same structure and equal length and has =stage turbine = 1 − z0 ) + hhs1 2g ρg ρg  rate and flow behavior, energy loss occurs in different stage turbines, approximately the same flow  Δvelocity pr1 p1 to c 2 − c12 the input velocity − pbe ω 2 Rin2 practice. 2 less causing the absolute output = = 2 than + ( z2 − z1 ) + hhr1 − (7)  2g 2g ρg  ρg  Δp Δp c2 − c2 ω2R2  s1 + r1 = 2 0 + ( z2 − z0 ) +（hhs1 +hhr1）− 2g 2g ρg  ρg

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Based on Equation (7), the mechanical energy loss in the first stage can be described by the following formula:

(hhs1 + hhr1 ) = (

c2 − c22 ∆ps1 ∆pr1 ω 2 R2 + )+ 0 + ( z0 − z2 ) + ρg ρg 2g 2g

(8)

Repeating the procedure described above, the overall mechanical energy loss of the multi-stage turbines can be written as: Z

∑ (hhsi + hhri ) = ∆p +

i =1

c20 − c2Z ω 2 R2 + ( z0 − z Z ) + Z 2g 2g

(9)

For the single-stage turbine, the torque of the blade in the stator is equal to the torque in the flow aisle but with opposite direction. Therefore, the torque can be obtained by considering the flow law of the fluid between the two blades. According to the theorem of the moment of momentum, the torque of the first stage turbine and the main axis is calculated as: M1 = ρQi R · (c1 cosα1 − c2 cosα2 ) = ρQi R · (c1u − c2u )

(10)

The output torque on the rotation shaft driven by the i-th-stage turbine is calculated as:     Mi = ρQi R · c(2i−1) cosα(2i−1) − c(2i) cosα(2i) = ρQi R · c(2i−1)u − c(2i)u

(11)

The transfer power consumption of the i-th-stage turbine blade is calculated as:     Ni = Mi ω = ρQi Rω · c(2i−1) cosα(2i−1) − c(2i) cosα(2i) = ρQi Rω · c(2i−1)u − c(2i)u

(12)

The torque of the multi-stage turbine (assuming the series is Z) is the sum of the torque of each single-stage; thus, the total output torque of the rotation shaft is given by:   Z      M = ρQi R · ∑ c(2i−1)u − c(2i)u i =1  Z      N = ρQi Rω · ∑ c(2i−1)u − c(2i)u

(13)

i =1

In comparison to Equation (13), the result is smaller than that calculated from the sum of the first single-stage turbine because the fluid has less energy. The method of collaborative simulation of the multi-stage turbine blades is important in predicting the performance of the turbine drill. 3. Design of the Turbodrill 3.1. Design Process of the Turbodrill Blade With the impregnated diamond bit, the Φ89 turbine is intended for drilling hot crystalline rock formations, for which the rock drillability classification number is from 7 to 8. The maximum downhole temperature is 120 ◦ C. Table 1 shows the functional parameters of the turbine. Table 1. Target performance parameters of the turbodrill (Φ89). Items/Unit

Value

Items/Unit

Value

Outside diameter/mm Working flow/L·s−1 Rotation speed/r·min−1

89 6–7 1800

Pressure drop/MPa Rated torque/N·m Drilling fluid density/kg·m−3

6–8 350 1000–2000

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The and profile designs, which areare keys to the design of the The blade bladedesign designincludes includesitsitsstructure structure and profile designs, which keys to the design of turbine drill. drill. As shown in Figure 4, the radial axialand sizeaxial are determined based on the formation the turbine As shown in Figure 4, theand radial size are determined based on the properties and rock drillability. The dimensionless coefficientcoefficient design method was [25] usedwas to formation properties and rock drillability. The dimensionless design[25] method determine the blade’s entrance exit structural The method Bezier curveofmodeling was used to determine the blade’sand entrance and exitangles. structural angles. of The method Bezier curve used to design the to corresponding blade profile, andprofile, a single-stage blade simulation was usedwas to modeling was used design the corresponding blade and a single-stage blade simulation conduct the partial correction; the simulation was conducted on the multi-stage blade, whose used to conduct the partial correction; the simulation was conducted on the multi-stage blade, whose outcomes outcomes were were used used to to forecast forecast the the turbodrill turbodrill overall overall performance. performance. The Thefinal finalmodified modified turbine turbine blades blades were manufactured to be used in the field test. were manufactured to be used in the field test. Dedsign aims according to formation conditions

Radial size Axial size

External dimensions of Turbine balde Dimensionless coefficient

Structural angle Blade profile Modification Simulation for single stage turbine Output performances prediction by multi-stage turbine simulation

Blade manufacture

Compration

Performances test Field application

Prediction methods

Figure Figure 4. 4. Design Designdiagram diagramfor forthe theturbodrill turbodrill blade. blade.

3.2. 3.2. Structure Structure Design Design of of the the Turbodrill Turbodrill Blade Blade The of the theturbine turbineblades bladesincludes includes the outer cylinder turbodrill the radial and The design design of the outer cylinder turbodrill sizesize andand the radial and axial axial the turbine; the parameters involved the design be checked. design principle sizessizes of theofturbine; the parameters involved in theindesign mustmust be checked. The The design principle is to is to maximize the flow area (orifice area) while ensuring adequate structural strength, thereby maximize the flow area (orifice area) while ensuring adequate structural strength, thereby improving improving the output energy. mechanical energy. The outer turbodrill cylinder is made steel tool for the output mechanical The outer turbodrill cylinder is made of special steel of forspecial the drilling the tool with anofouter and the shell is 8 mm. For the shell withdrilling an outer diameter Φ89 diameter mm, and of theΦ89 shellmm, thickness is 8 mm.thickness For the shell material, 40CrMo, material, 40CrMo, which has high mechanical properties and better heat-treated properties, is which has high mechanical properties and better heat-treated properties, is selected. selected. The rotation shaft is a solid axis for bearing the drill bit torque, rotor torque, and axial weight The rotation is ainner solid diameter axis for bearing the drill torque, rotorboth torque, and axial weight on on bit (WOB). Theshaft rotor’s determines the bit shaft diameter, of which work through bit (WOB). The rotor’s inner diameter determines the shaft diameter, both of which work through the the clearance fit. The solid shaft torsional stress suffered should be less than the allowable twisting clearance fit.axial The solid torsional stress suffered should be less conditions. than the allowable twisting stress. stress. The loadsshaft suffered should meet the column stability The rotation shaft can The axial loads suffered should meet the column stability conditions. The rotation shaft can be be considered as the compressive column under the bit’s weight. The axial load of rotation shaft considered as the compressive column under the bit’s weight. The axial load of rotation P shaft 4Pshould should meet the stability of column, and the stress should satisfy the formulas, σ = ϕA = ϕπd2 ≤ σp . P 4P meet the stability of column, should satisfy calculated the formulas, σ= = ≤ σ p . The The diameter should be larger and thanthe thestress maximum diameter by different demands: ϕ A ϕπ d 2 s s (diameter ) by different demands: diameter should be larger than the maximum calculated 4P 3 [S] · T 2 d ≥ Max , (14) ϕπσp   [ S []τ⋅]T 4P  d ≥ Max  3 ,2 (14) 



[τ ]

ϕπσ p 

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The radial size of the turbodrill blade is excessively large. Considering the casting difficulty and strength, the radial thickness of the thinnest part is 1.25 to 3 mm. To To prevent interference between the static and dynamic components and considering the precision, the clearance between the stator parts 1.25 mm. mm. Figure 5 shows the partial design parameters and radial and rotor is selected to be 0.75 to 1.25 sizes selected.

11

30

30

11

40 37.5 36 30

60 62.5 64 70

Figure 5. Design dimensions (mm).

Profile Design Design 3.3. Turbine Blade Profile The turbine turbine blade bladeprofile profilecan caninfluence influencethe the flow field of the path by changing the mud velocity flow field of the path by changing the mud velocity and and pressure distribution. To reduce fluid friction loss, the profile line of the blade should be pressure distribution. To reduce fluid friction loss, the profile line of the blade should be continuously continuously such that thepressure blade surface pressure canWhen vary changed such changed that the blade surface distribution anddistribution velocity canand varyvelocity smoothly. smoothly. When calculating theflow incompressible flow field, uniform field is used to describe calculating the incompressible field, the uniform flowthe field is usedflow to describe the evolution of the evolution of pressure and velocity according to physical space and time. The available mass pressure and velocity according to physical space and time. The available mass conservation equations conservation equations and can the be momentum equation be derived according the equations unsteady and the momentum equation derived according to can the unsteady boundary layertobasic boundary layerfor basic of motion flow the incompressible fluid. The boundary of motion flow theequations incompressible fluid. Thefor boundary curvature radius R has a greatercurvature influence radius R has The a greater on thehave fluid. The blade surface should have atocontinuous curvature on the fluid. blade influence surface should a continuous curvature derivative maintain the smooth derivative toofmaintain smooth distribution of the speedthat andthe pressure of the distribution the speedthe and pressure of the blade. Assume blade-type lineblade. is y =Assume f (x), andthat the the blade-type line is y = f(x), and the type of line curvature and third derivatives are, respectively: type of line curvature and third derivatives are, respectively: C=

1

y ''00

=

=

y

f ''

f 00

3 3 C = R1R = = 3 2 3 2 11++( y 0' 2 22 1 + f ' 0 22 2 [ ( y )) ]  [1(+( f) ) ]

h

i

f ''' 1f 000+ (1f+( ' ) f0 )− 3−f 3' (f 0f( ''f )00 )  CC = = 2

2

2

2

(15) (15)

5 5 0 2 2

f2 ) 1 +[1( +( f ')  2 ]  

Although the combined line can satisfy the continuously shrinking demands of the inlet, outlet Although the combined line can satisfy the continuously shrinking demands of the inlet, outlet and channel of the blade, there is often a discontinuous curvature derivative point at the junction of the and channel of the blade, there is often a discontinuous curvature derivative point at the junction of curve that can cause nutation of the flow velocity and pressure and reduce the hydraulic characteristics the curve that can cause nutation of the flow velocity and pressure and reduce the hydraulic of the turbine. Therefore, this design uses a combination of computer-aided design and configuration characteristics of the turbine. Therefore, this design uses a combination of computer-aided design Bezier blade profile to eliminate the catastrophe point. Based on the semi-circular arc of the head and configuration Bezier blade profile to eliminate the catastrophe point. Based on the semi-circular and trail edge, the blade profile of the stator and rotor is designed as shown in Figure 6. The turbine arc of the head and trail edge, the blade profile of the stator and rotor is designed as shown in Figure 6. blade profile, which is described by the data array, can be easily manufactured using a numerical The turbine blade profile, which is described by the data array, can be easily manufactured using a control machine. numerical control machine.

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9 of 17 of 18 18 99 of

X X

yp yp ys ys

xx yp yp ys ys

Rotor Rotor 10 10 11 11

9.81 9.81

10 10 11 11

Stator Stator

0.1228 0.1228 0.3404 0.3404 0.6108 0.6108 0.8895 0.8895 1.1516 1.1516 1.3328 1.3328 1.5083 1.5083 1.7622 1.7622 2.0887 2.0887 2.4897 2.4897 2.9664 2.9664 3.5135 3.5135 4.1167 4.1167

YYpp

6.6244 6.6244 6.8909 6.8909 7.0954 7.0954 7.2406 7.2406 7.3228 7.3228 7.3368 7.3368 7.3415 7.3415 7.3498 7.3498 7.3651 7.3651 7.3957 7.3957 7.4585 7.4585 7.5787 7.5787 7.7847 7.7847

X YYss X X YYpp X X X 9.7169 13.6305 4.7487 8.0932 5.5339 9.7169 13.6305 4.7487 8.0932 5.5339 9.8501 13.6757 5.3833 8.504 4.7754 9.8501 13.6757 5.3833 8.504 4.7754 9.9908 13.6741 5.9985 8.9996 3.9831 9.9908 13.6741 5.9985 8.9996 3.9831 10 12.7613 6.5802 9.5532 3.1941 10 12.7613 6.5802 9.5532 3.1941 9.9529 12.4545 7.1205 10.1375 2.4549 9.9529 12.4545 7.1205 10.1375 2.4549 9.48 11.5649 7.6144 10.7267 1.8133 9.48 11.5649 7.6144 10.7267 1.8133 9.1787 10.9982 8.0582 11.2974 1.3042 9.1787 10.9982 8.0582 11.2974 1.3042 8.8351 10.3619 8.4532 11.8359 0.9454 8.8351 10.3619 8.4532 11.8359 0.9454 8.4349 9.6757 8.7915 12.3188 0.7332 8.4349 9.6757 8.7915 12.3188 0.7332 7.9774 8.9617 9.071 12.7317 0.3615 7.9774 8.9617 9.071 12.7317 0.3615 7.4603 8.2385 9.29 13.0635 0.1036 7.4603 8.2385 9.29 13.0635 0.1036 6.8811 7.5262 9.4469 13.3057 0 6.8811 7.5262 9.4469 13.3057 0 0.1228 6.8471 9.5407 13.452 0.0068 0.1228 6.8471 9.5407 13.452 0.0068

YYss

6.2276 6.2276 5.6988 5.6988 5.2916 5.2916 5.0298 5.0298 4.9145 4.9145 4.9209 4.9209 5.0035 5.0035 5.1092 5.1092 5.1928 5.1928 5.4265 5.4265 5.7551 5.7551 6.1206 6.1206 6.2994 6.2994

xx

Coordinate System System for for Turbodrill Turbodrill Profile Profile Coordinate

9.81 9.81

Figure 6. 6. Turbine Turbine blade blade profile profile(mm). (mm). profile (mm). Figure

4. Numerical Numerical Simulation Simulation and and Test Test 4. 4. Numerical Simulation and Test 4.1. CFD CFD Model Model of of the the Turbodrill TurbodrillBlade Blade Turbodrill Blade 4.1. The single single blade-to-blade blade-to-blade flow flowfield fieldmode modeis ismainly mainlyused used to to simulate simulate aaa blade. blade. The The model model ignores ignores The blade-to-blade flow field mode is mainly used to simulate blade. the mutual interference between the blades and the influence of the rotor blades on the flow field. In the rotor blades onon thethe flow field. In the mutual interference interference between betweenthe theblades bladesand andthe theinfluence influenceofof the rotor blades flow field. addition, a single runner blade model will set be as a standard quadrilateral, which has a different addition, a single runner blade In addition, a single runner blademodel modelwill willset setbe beasasaastandard standardquadrilateral, quadrilateral, which which has a different exit compared to the actual field case. Thus, the simulation results are substantially different than than the the compared to to the actual field case. Thus, the simulation results are substantially different exit compared field results. field results. results. field In this this paper, paper, we use single-stage turbine blade simulation to improve improve the blade blade design. The turbine blade simulation to the design. The In paper, we weuse useaa asingle-stage single-stage turbine blade simulation to improve the blade design. multi-stage and multi-blade multi-blade turbodrill is used used to predict the performance. performance. First, aa First, single-cycle turbine multi-stage and turbodrill is predict the First, single-cycle turbine The multi-stage and multi-blade turbodrill is to used to predict the performance. a single-cycle blade in the two-dimensional model is drawn in Bladegen. Next, a two-dimensional model of an an blade inblade the two-dimensional modelmodel is drawn in Bladegen. Next,Next, a two-dimensional model of turbine in the two-dimensional is drawn in Bladegen. a two-dimensional model of annular array of the turbine blade in a single stage is formed, extending upward and downward to annular array of the turbine blade in a single stage is formed, extending upward and downward to an annular array of the turbine blade in a single stage is formed, extending upward and downward toaa time length ofofthe the blade. An import and export boundary flow channel is implemented, implemented, forming forming aa atime timelength lengthof theblade. blade.An Animport importand andexport exportboundary boundary flow flow channel channel is closed fluid channel. A single-stage multi-blade flow model is obtained. Next, the three-dimensional channel. A single-stage multi-blade flow model is obtained. Next, the three-dimensional closed fluid channel. model is implemented into ANSYS ANSYS through through Bladegen Bladegen to to form form the the single-stage single-stage multi-blade multi-blade CFD CFD implemented into Bladegen form the single-stage multi-blade model is implemented simulation model shown in Figure 7. model shown shown in in Figure Figure 7. 7. simulation model

(a) (a)

(b) (b) Figure 7. 7. Simulation Simulation model model of of the the turbodrill turbodrill blade. blade. (a) (a) Single-stage Single-stage blade blade model; model; (b) (b) Multi-stage Multi-stage and and Figure Figure 7. Simulation model of the turbodrill blade. (a) Single-stage blade model; (b) Multi-stage and multi-blade model. multi-blade model. model. multi-blade

4.2. Meshing Meshing and and Boundary Boundary Conditions Conditions 4.2. In the the simulation, simulation, the the stator stator and and rotor rotor are are meshed meshed using using the the full full flow flow path path method. method. The The In multistage turbine stators and rotors are stacked according to the actual assembly. Different grid multistage turbine stators and rotors are stacked according to the actual assembly. Different grid

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4.2. Meshing and Boundary Conditions In the simulation, the stator and rotor are meshed using the full flow path method. The multistage turbine stators Energies 2016, 9,and 1035 rotors are stacked according to the actual assembly. Different grid coordinates 10 of 18 are set to each level. The boundaries of the rotor can be set to a controllable speed value. The partial coordinates are set to eachencrypted, level. The boundaries of the rotor can set to a controllable speed value. profile wire is intelligently and the grid nodes andbeelements can be adjusted to ensure The partial profile wire is intelligently encrypted, and the grid nodes and elements can berotor adjusted sufficient accuracy of the flow field. Because the field flow is turbulent, the stator and grid cell to ensure sufficient accuracy of the flow field. Because the field flow is turbulent, the stator and rotor are all hexahedral meshes, as shown in Figure 8. Different models must set different borders according grid cell are all hexahedral meshes, as shown in Figure 8. Different models must set different borders to theaccording difference between the flow fields in ANSYS. Because the three-dimensional flow field in this to the difference between the flow fields in ANSYS. Because the three-dimensional flow simulation is continuously turbulent flow, the calculation of the control theory should field in this simulation isdifferentiable continuously differentiable turbulent flow, the calculation of the control use turbulence theory. In addition, the In default equation is theequation Reynolds equation. theory should use turbulence theory. addition, the default is the Reynolds equation.

(a)

(b)

Figure 8. Finite element model after meshing. (a) Meshing of the stator; (b) Meshing of the rotor.

Figure 8. Finite element model after meshing. (a) Meshing of the stator; (b) Meshing of the rotor.

Table 2 plots the meshing of the single and multi-stage turbine simulation. The drilling mud has

Table 2 plots theand meshing of the single multi-stage simulation. The drilling mud has a certain density viscosity. During theand simulation, Fluidturbine is selected as the condition to analyze thesedensity two constants. Other analysis parameters are generally by defaultasinthe ANSYS. Afterto these a certain and viscosity. During the simulation, Fluidset is selected condition analyze DefineOther Run isanalysis used to perform the corresponding of the calculation results. Inthese theseprocedures, two constants. parameters are generallyanalysis set by default in ANSYS. After ANSYS CFD-Post, the corresponding calculation result can be used in the Insert function to obtain procedures, Define Run is used to perform the corresponding analysis of the calculation results. the blade velocity field and pressure field. In ANSYS CFD-Post, the corresponding calculation result can be used in the Insert function to obtain the blade velocity field and pressure field. Table 2. Mesh number of divisions for single stage and multistage turbodrill blade. Grid Number of Nodes Number of Units of Hexahedrons Table 2. Mesh number of divisions for single stage and multistage Number turbodrill blade.

Single flow passage of stator 133,325 Full flow passage of stator 133,325 × 16 Number133,325 of Nodes SingleGrid flow passage of rotor Full flow passage of rotor 133,325 Single flow passage of stator 133,325 × 16 Flow passage of single stage multi-blade 1,333,250 × 32 Full flow passage of stator 133,325 × 16 Flow passage of multi-stage 1,333,250 Single flow passage of rotormulti-blade 133,325 × 160

Full flow passage of rotor Flow of singleof stage 4.3.passage Test Principle the multi-blade Turbodrill Flow passage of multi-stage multi-blade

133,325 × 16 1,333,250 × 32 1,333,250 × 160

121,920 121,920 × 16 Number of Units 121,920 121,920 × 16 121,920 1,219,200 121,920 ××3216 1,219,200 × 160 121,920

121,920 121,920 × 16 Number 121,920of Hexahedrons 121,920 ×121,920 16 1,219,200 × 32 × 16 121,920 1,219,200 ×121,920 160

121,920 × 16 1,219,200 × 32 1,219,200 × 160

121,920 × 16 1,219,200 × 32 1,219,200 × 160

As shown in Figure 9, a high-pressure three-throw reciprocating pump is used in the drilling mud circulation system. A certain high-pressure mud is output through the manifold to drive the 4.3. Test Principle of the Turbodrill Φ89 drill to rotate and penetrate. The circulation system can also ensure that the mud is cleaned and As shown in Figure 9, test a high-pressure three-throw pump is used the drilling return it to the pool. The bench is primarily composedreciprocating of the turbine drill support andininvolves holding, lifting otherhigh-pressure basic operations. Theis power head on the slide is used to provide mudrighting, circulation system. Aand certain mud output through the manifold to drive the continuously WOB toThe the circulation bottom of the turbinecan drill bit ensure as well as some torque and Φ89 drill to rotateadjustable and penetrate. system also that therotational mud is cleaned to drive the turbodrill. return it to the pool. The test bench is primarily composed of the turbine drill support and involves

righting, holding, lifting and other basic operations. The power head on the slide is used to provide continuously adjustable WOB to the bottom of the turbine drill bit as well as some rotational torque to drive the turbodrill. The control system can be used to measure the WOB, pressure, flow, rate of penetration (ROP), footage, output torque, and speed equal amount in real time. The mud pump flow rate can be adjusted continuously. The results can be displayed on the display simultaneously. The control system is also equipped with the function of a security alarm in case of emergency. The data can be saved in real time to facilitate off-line analysis and synthesis.

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Figure 9. 9. Test Test principle principle of of the the turbodrill: turbodrill: 1: 1: support support frame; frame; 2: 2: power power head; head; 3: 3: turbodrill; turbodrill; 4: 4: centralizer; centralizer; Figure 5: rock box; 6: mud pool; 7: wall; 8: drilling mud pump. 5: rock box; 6: mud pool; 7: wall; 8: drilling mud pump.

The control system be used tousing measure WOB, pressure, flow, rate The of penetration (ROP), test works can can be conducted the the cross multiplication method. main parameters footage, output torque, and speed equal amount in real time. The mud pump flow rate can be can be changed to test the output performances. Different WOB levels are exerted on different types adjusted The results be displayed display[29]. simultaneously. Thebetween control of granitecontinuously. blocks. The turbine outputcan torque and speed on arethe measured The relationship system is also equipped withamount the function of a security alarm in case of emergency. The can be import and export the same of pressure, research output torque and efficiency ofdata the turbine saved in real time to facilitate off-line analysis and synthesis. drill speed. The test works can be conducted using the cross multiplication method. The main parameters 5. Result and Discussion can be changed to test the output performances. Different WOB levels are exerted on different types of granite blocks. The turbine output torque and speed are measured [29]. The relationship between 5.1. Simulation of a Single-Stage Turbodrill Blade import and export the same amount of pressure, research output torque and efficiency of the turbine Figure 10 plots the pressure and flow cloud diagram of the single-stage turbine when the flow drill speed. rate is 6 L/s. As shown in the figure, there are the two different directions after the drilling mud flows 5. Result and Discussion into the path: one toward the suction surface of the stator, and the other toward the pressure surface of blade. The velocity of the drilling mud in the stator and rotor is nearly zero at the leading edge 5.1. of a Single-Stage andSimulation trailing edge. The pressureTurbodrill at the theBlade velocity at the surface is often greater than the flow rate of the suction surface. The pressure and flow not the produce Figure 10 plots the pressure and flow cloud cloud diagram diagramof ofthe thesingle-stage single-stageturbine turbinedid when flow stalls and other anomalies, thereby proving that the profile shape is reasonable and meets all the rate is 6 L/s. As shown in the figure, there are the two different directions after the drilling mud of flows design into therequirements. path: one toward the suction surface of the stator, and the other toward the pressure surface As shown in the figure of the pressure afterand drilling into zero the flow path, the difference of blade. The velocity of the drilling mud in field, the stator rotormud is nearly at the leading edge and in the pressure distribution the pressure suction surface theflow stator blade is trailing edge. The pressure atbetween the the velocity at thesurface surfaceand is often greater thanofthe rate of the relatively small. When the drilling mud flows through the rotor blades, the pressure surface and suction surface. The pressure and flow cloud diagram of the single-stage turbine did not produce suction surface impactedthereby by the pressure In addition, the pressure of the pressure surface stalls and otherare anomalies, proving field. that the profile shape is reasonable and meets all ofwas the significantly lower than the pressure of the suction surface, where a large pressure difference exists. design requirements. This process contributes to the rotor blade moving toward to the pressure surface, thereby providing the impetus for the torque generated. The output characteristics of the turbine blade can be obtained by using the CFX software, as shown in Figure 11. According to the simulation results, the working brake torque of the single-stage turbine is 1.8 N·m. Under normal operating speed, the torque is 1.5–2 N·m, the maximum power is 0.19 kW, the speed can reach up to 3800 r/min when idle, and the optimal operating speed is approximately 1800 r/min. At the designed operating speed, the pressure of the power section can likely drop to 0.029–0.032 MPa, which does not substantially contribute to the speed change. This result corresponds with the theoretical value, which is less than the design value of 0.03–0.04 MPa.

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(a)

(b) Figure 10.Cloud diagram of the single-stage turbodrill blade. (a) Pressure cloud diagram; (b) Flow

Figure 10. Cloud diagram of the single-stage turbodrill blade. (a) Pressure cloud diagram; (b) Flow velocity cloud diagram. velocity cloud diagram. Energies 9, 1035 As2016, shown in the

13 of 18 figure of the pressure field, after drilling mud into the flow path, the difference in the pressure distribution between the pressure surface and suction surface of the stator blade is Power/Kw relatively small. the pressure OutputWhen Torque/the N.mdrilling mud flows through the rotor blades, Pressure loss/MPa surface and suction surface addition, the pressure of the pressure surface 2.0 are impacted by the pressure field. In 0.24 0.10 Output Torque/ N.m was significantly lower than the pressure of the suction surface, where a large pressure difference Power/ Kw Pressure loss/ MPa to the pressure exists. This process contributes to the rotor blade moving toward surface, thereby 0.20 1.6 0.08 providing the impetus for the torque generated. The output characteristics of the turbine blade can be obtained by using 0.16 the CFX software, as shown in Figure 11. According to the simulation results, the working brake torque of0.06 the single-stage 1.2 turbine is 1.8 N·m. Under normal operating speed, the torque is 1.5–2 N·m, the maximum power is 0.12 0.19 kW, the speed can reach up to 3800 r/min when idle, and the optimal operating speed is 0.8 0.04 section can approximately 1800 r/min. At the designed operating speed, the pressure of the power 0.08 likely drop to 0.029–0.032 MPa, which does not substantially contribute to the speed change. This result corresponds with the theoretical value, which is less than the design value of 0.03–0.04 MPa. 0.4 0.02

0.04

0.0 0

500

1000

1500

2000 2500 3000 Rotation speed/ RPM

3500

0.00 0.00 4000 4500

Figure 11. Simulated outputperformances performances of turbodrill blade. Figure 11. Simulated output ofthe thesingle-stage single-stage turbodrill blade.

5.2. Simulation of the Multistage Turbodrill Blade In previous studies, it is assumed that the boundary conditions are the same at each stage when the single-stage turbine simulation is conducted to predict the overall performance. However, energy loss occurs in each stage. In addition, the speed direction of the outlet boundary of the rotor will change, thus affecting the flow field considerably. Therefore, the inlet and outlet speeds of the first-

0.08 0.4

0.0 Energies 2016, 9, 1035 0

0.04

500

1000

1500

2000 2500 3000 Rotation speed/ RPM

3500

0.02

0.00 0.00 4000 4500

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11. Simulated outputBlade performances of the single-stage turbodrill blade. 5.2. Simulation of theFigure Multistage Turbodrill

In studies, it is assumed thatBlade the boundary conditions are the same at each stage when 5.2.previous Simulation of the Multistage Turbodrill the single-stage turbine simulation is conducted to predict the overall performance. However, energy In previous studies, it is assumed that the boundary conditions are the same at each stage when loss occurs in each turbine stage. simulation In addition, the speedtodirection the outlet boundary of theenergy rotor will the single-stage is conducted predict theof overall performance. However, change, thus affecting the flow field considerably. Therefore, the inlet and outlet speeds of the firstloss occurs in each stage. In addition, the speed direction of the outlet boundary of the rotor will and second-stage turbine is different. As a result, a simple simulation involving multiplying the results change, thus affecting the flow field considerably. Therefore, the inlet and outlet speeds of the firstandstage second-stage turbine isandifferent. a result, aofsimple simulation involving multiplying the of every cannot provide accurateAs prediction the output performance. results of every turbine stage cannot provide an accurate prediction of the output performance. A multi-stage simulation can overcome this drawback and better simulate the actual A As multi-stage canflow overcome thisthe drawback and better simulateofthe conditions. shown inturbine Figuresimulation 12, when the is 6 L/s, inlet and outlet pressures theactual first- and conditions. As shown in Figure 12, when the flow is 6 L/s, the inlet and outlet pressures of the firstsecond-stage turbodrill blades are different, and the pressure or velocity of flow of the second-stage and second-stage turbodrill blades are different, and the pressure or velocity of flow of the secondturbodrill blade is smaller than that of the first stage. In addition, the pressure or velocity of flow of the stage turbodrill blade is smaller than that of the first stage. In addition, the pressure or velocity of subsequent stage turbodrill blade is smaller than that of the previous stage, and this trend continues flow of the subsequent stage turbodrill blade is smaller than that of the previous stage, and this trend for the increasing stages, with progressive decreases in pressure velocity. continues for the increasing stages, with progressive decreases in and pressure and velocity.

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(b) Figure 12. Cloud diagram of the multi-stage turbodrill blade. (a) Pressure cloud diagram; (b) Flow

Figure 12. Cloud diagram of the multi-stage turbodrill blade. (a) Pressure cloud diagram; (b) Flow velocity cloud diagram. velocity cloud diagram.

5.3. Comparison with the Experimental Results Data A represent the simple product of the result obtained by the single-stage output and the number of turbine stages. Data B represent the machine's performance, which is transformed by the five-stage simulation results and the number of turbine stages, while considering the interaction between the multi-stage turbodrill blades. Data C are the experimental measured data of the turbodrill. Data D are the design aims of the turbodrill. In comparison to design aim D, C represents the practical

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5.3. Comparison with the Experimental Results Data A represent the simple product of the result obtained by the single-stage output and the number of turbine stages. Data B represent the machine’s performance, which is transformed by the five-stage simulation results and the number of turbine stages, while considering the interaction between the multi-stage turbodrill blades. Data C are the experimental measured data of the turbodrill. Data D are the design aims of the turbodrill. In comparison to design aim D, C represents the practical overall performance of the turbo-drill prediction, which is obtained from the drilling test. Figure 13 plots overall performance of the Φ89 mm turbo-drill predictions, including torque, power, and pressure drop, with the change in rotation speed. The optimum operating actual speed is found to be in the range of 900–1800 r/min based on the multi-level simulation and experimental measurement. The torque fluctuates in the range of 200–300 N·m, and the power is in the range of 25–38 kW. Regarding the value of the torque prediction, the overall outcome of the multi-stage simulation is less than that of the single-stage, with a deviation of 3–16 N·m. The maximum driven torque of the turbodrill is from data D, followed by the values from data A and data B; the minimum value is from data C. Thus, the outcome of the multi-stage simulation is closer to the real performance given by data C.Data D are the design aims of the turbodrill, which are generally idealized. Data A are the results from one single stage multiplied by the number of stages, which are remarkably close to the design aims, but far from the actual experimental value. The results from the total n-stages geometry simulated (Data B) are close to the experimental value. That is to say, the outcome of the multi-stage simulation has the highest accuracy. We recommend this method for predicting the performance of Energies 2016, 9, 1035 15 of 18 the turbodrill. 400 40 Output torque,D>A>B>C

14 300 Output Torque /Nm

Power /kW

30 25

200

20 15

Pressure loss,C>B>D>A

0

0

Power,D>A>B>C

0

1000

2000

10 8 6

100

10 5

12

3000

4000

4

Pressure Loss /MPa

35

2 0

Rotation Speed /RPM Figure 13. Comparison between the experimental results and predicted values. Figure 13.Comparison between the experimental results and predicted values.

The power in the multi-stage simulation is higher thatthan of the single-stage simulation. powerpredicted predicted in the multi-stage simulation is than higher that of the single-stage The deviation between data C and data D is modest, in the range of 0–1 kW. The comparative simulation. The deviation between C and data D is modest, in the range of 0–1 kW. The experiments illustrate thatillustrate the overall is D >trend A>B simulation result is comparative experiments thattrend the overall is >DC. > AThe > Bmulti-stage > C. The multi-stage simulation closer realtotest Regarding pressurethe drop, the result of the multi-stage is result to is the closer theresult. real test result. the Regarding pressure drop, result of thesimulation multi-stage higher than is that of thethan single-stage with asimulation, deviation ofwith 0–1 MPa. The comparative studies simulation higher that of simulation, the single-stage a deviation of 0–1 MPa. The demonstrated that the overall pressure predicted follows thepredicted trend of C > B > the D >trend A, with the> comparative studies demonstrated that drop the overall pressure drop follows of C multi-level simulation prediction being closer to the real test measured performance values of data C. B > D > A, with the multi-level simulation prediction being closer to the real test measured Overall, the results multi-stage be multi-stage used to predict the performance parameters. performance valuesof ofthe data C. Overall,simulation the resultscan of the simulation can be used to predict The multi-stage simulation method has the highest accuracy. We can analyze these results based the performance parameters. on the following explanations. thehas inertial centrifugal forceWe is considered modify Bernoulli The multi-stage simulationFirstly, method the highest accuracy. can analyzetothese results based on the following explanations. Firstly, the inertial centrifugal force is considered to modify Bernoulli Equation in the same streamline for per unit weight of the drilling mud. According to Equation (6), the energy in this situation is smaller than normal. Secondly, the coupling effect between different stage turbodrill blades is considered in the multistage simulation, which enables the flow field much closer to the real. Finally, the traditional method for the single-stage simulation and design has some

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Equation in the same streamline for per unit weight of the drilling mud. According to Equation (6), the energy in this situation is smaller than normal. Secondly, the coupling effect between different stage turbodrill blades is considered in the multistage simulation, which enables the flow field much closer to the real. Finally, the traditional method for the single-stage simulation and design has some inevitable defects. Herein a new design and performance prediction method for turbodrill are put forward in this paper to enhance the accuracy. I believe that this method will have great application. 6. Conclusions (1)

(2)

(3)

(4)

A Φ89 mm turbodrill blade was developed for high-temperature geothermal drilling of granite formations using a Bezier curve design. The single- and multi-blade turbine simulation was used to achieve the optimization and correction of the turbine profile. The relevant manufacturing and assembly work were also completed. The output characteristics of a turbine blade model were established based on the gravitational and rotation centrifugal field, using the Bernoulli equation and the momentum theorem. The traditional model was modified, and the accuracy of turbine performance prediction was improved. The turbodrill has 200 stages. The braking torque can reach 341 N·m. The maximum speed is approximately 3800 r/min, and the maximum power is approximately 38 kW. The rated speed is approximately 1800 r/min, and the pressure drop is less than 8 MPa, consistent with the theoretical design and meeting the design requirements. Based on the multi-stage simulation and optimization interval theory, the entire range of fluctuation of the optimum operating actual speed is 900–1800 r/min, and the torque fluctuates in the range of 200–300 N·m. The power fluctuates over the range of 25–38 KW, which reaches the level of the highest efficiency turbine, i.e., it is the best working range. The multi-stage simulation was used to predict the turbodrill output performance by comparing the single-stage turbine simulation and the entire real analysis; the multi-stage simulation was found to be closer to the truth, i.e., it is more accurate than the single-stage simulation. The multi-stage simulation is a suitable method for predicting the performance parameters.

Acknowledgments: This work is supported by the National Natural Science Foundation of China (No. 41572360), the Fundamental Research Funds for the Central Universities (No. 292015061), and the National Key Technology Support Program (No. 2015BAD20B02). We sincerely acknowledge the former researchers for their excellent works, which greatly assisted our academic study. Author Contributions: Yu Wang and Bairu Xia established the hydrodynamic model of turbodrill blade. Yu Wang and Zhiqiao Wang conceived and designed the experiments and wrote the paper. Zhiqiao Wang performed the experiments, Qin Zhou analyzed the data, and Liguang Wang contributed to the simulation results for the turbodrill blade. Conflicts of Interest: The authors declare no conflicts of interest.

Nomenclature X, Y, and Z ω r W z p u E0 and E1 p0 and p1 c0 and c1

unit mass gravity of the x-axis, y-axis and z-axis, respectively, N/m angular velocity of the revolving turbodrill blade, rad/s radius of the point A, m potential function produced by mass, m3 /s height of point A, m pressure of point A, pa flow rate of the drilling mud with respect to the turbodrill blade, m/s energy of the drilling mud at the inlet and outlet of the first-stage turbodrill stator, respectively pressure of the drilling mud at the inlet and outlet of the first-stage turbodrill stator, respectively, Pa absolute speed of the drilling mud at the inlet and outlet of the first-stage turbodrill stator, respectively, m/s

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z0 and z1 hhs1 E2 p2 c2 z2 hhr1 Z Z

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height of the drilling mud at the inlet and outlet of the first-stage turbodrill stator, respectively, m mechanical energy loss of the first-stage turbodrill stator, m energy of the drilling mud at the outlet of the first-stage turbodrill rotor pressure of the drilling mud at the outlet of the first-stage turbodrill rotor, Pa absolute speed of the drilling mud at outlet of the first-stage turbodrill rotor, m/s height of the drilling mud at outlet of the first-stage turbodrill rotor, m mechanical energy loss of the first-stage turbodrill rotor, m series of the multi-stage turbodrill blades

∑ (hhsi + hhri )

total mechanical energy loss of the turbodrill

∆p cZ zZ d T [S] [τ ] P ϕ σp WOB ROP

total pressure loss of turbodrill, pa absolute speed of the drilling mud at the outlet of the Z stage turbodrill rotor, m/s height of the drilling mud at outlet of the Z stage turbodrill rotor, m diameter of the rotor shaft, mm torque on the rotor shaft, N·mm safety factor of the shaft materials allowable twisting stress, MPa weight on the bit, N reduction factor according to the flexibility of the shaft allowable stress for the strength calculation, N/cm2 weight on bit rate of penetration

i =1

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