1 © 2019 by ASME

Proceedings of IMECE2019

International Mechanical Engineering Congress & Exposition

IMECE2019

November 11-14, 2019, Salt Lake City, Utah, USA

IMECE2019-10636

DESIGN OF A TURBOPISTON PUMP GUIDED BY COMPUTATIONAL ANALYSIS

Ting Wang Patrick W. Rousset Energy Conversion and Conservation Center Power Engineering, lnc. University of New Orleans New Orleans, LA 70123 New Orleans, LA 70461

ABSTRACT

An innovative pump, TurboPiston Pump (TPP), has been

invented to incorporate the merits of centrifugal, axial, and

positive displacement pumps. The TPP is designed to deliver

large flow rates with a potential at high pressure of up to 1000

psia with one stage. To improve the original design, an

understanding of the flow behavior inside the pump is needed.

The objective of this study is to simulate the flow field inside the

pump and study its performance to guide the design process.

This study includes modeling the pump with the transient sliding

mesh scheme using a commercial computational fluid dynamics

solver, ANSYS/FLUENT. The flow pattern, static pressure

distribution, and total pressure losses are calculated and analyzed.

The regions of high total pressure losses and potential creation

of cavitation are identified. A plastic demonstration model and a

metal prototype have been fabricated based on the result of the

CFD analyis.

1 INTRODUCTION

The destruction caused by Hurricane Katrina in 2015 in

New Orleans has brought attention to the limited capability of

existing pumps -- high-pressure pumps deliver small flow rates,

while high-flow pumps deliver low-pressure head. The high-

pressure, low flow rate pumps, including piston pumps or screw

pumps, employ positive displacement motion while. the high-

flow, low-pressure pumps employ axial or centrifugal flow

pumps. For example, the flow rate of a typical drainage pump

used in New Orleans is 750 cfs; and the pressure head is only 40

ft, which is sufficient only for pumping water over the levees,

rather than pumping water directly into Lake Pontchartrain. Due

to these limitations, canals were implemented in Greater New

Orleans to drain large volumes of flood water several miles from

the center of the city to Lake Pontchatrain. The breach of a

dozen of these levees along these canals has prompted the need

to look into alternative means to resolve future flood problems.

To this end, the second author invented the TurboPiston

Pump (TPP) that incorporates the merits of centrifugal, axial,

and positive displacement pumps to deliver large flow rates

capable of reaching very high pressure of up to 1000 psia with a

single stage. Although the TPP could solve part of the New

Orleans drainage and flood problem, the unique feature of TPP

can be broadly used in many industries including gas/oil,

petrochemical, pharmaceutical, power, agricultural irrigation,

food, textile, deep-sea drilling, hydraulic fracturing of shale

gas/oil, fire engine applications, and river/costal dredging, etc.

1.1 Background It has been more than 100 years since A. Baldwin Wood

invented the revolutionary 12-foot screw pump in 1913 [1]. The

Wood Screw Pump resolved New Orleans's drainage problems

and uniquely contributed to the health and wealth of New

Orleans' environmental and commercial foundations. The Wood

pumps were, however, designed only for drainage and not for

saving the city from fast and massive flooding. The Wood Screw

Pump is characterized by high volume and low pressure for

lifting a large amount of water 40 feet over the levee and

dumping it into canals connected to Lake Pontchartrain.

Because multiple stages must be used to reach high

pressures, the existing centrifugal pumps can offer a bit more

pressure but not much more than 300 feet of water head before

their efficiencies drop significantly to below 50%. The

disadvantage of the Wood pumps and the centrifugal pumps is

that they must be located near the dump sites; therefore, canals

became necessary and stretched from the inner city to Lake

Pontchartrain. The breach of a dozen levees along the canals led

to the shocking tragedy of Katrina which could have been

prevented if those canals were not there.

Another type of traditional pump, the piston pump, delivers

very high pressure flow. Unfortunately, its volume flow rate is

unacceptably low (less than 5% of the centrifugal pump of

equivalent size). Hence, one of the solutions to the current

pump’s limitations is the invention of a high- pressure, high-

volume pump that bypasses the canals and pumps water directly

into the Mississippi River or Lake Pontchartrain.

The TPP consists of two opposing rotating disks (see Fig. 1)

with the suction-side disk mounted with a slight inclined angle

so that these two disks are separated with a wedge of volume.

Eight pistons are built on the inclined suction disk, and eight

corresponding cylinders are built on the vertical discharging disk.

Each chamber includes associated suction and discharge valves

and rotates as an integral part of each rotor. The rotating motion

will drive a continuous piston motion of compression and

2 © 2019 by ASME

expansion as the pistons and cylinders combine on the

circumference of a circle and glide in and out of each other. The

pump works by sucking fluid into the intake, as seen in the first

panel of Fig. 1 at location (1) where it flows through a

centrifugal impeller. The impeller boosts the head pressure (2)

via centrifugal force before entering into the valves of the

cylinder assembly (3). This effectively allows the fluid to flow

at higher rates while decreasing the chances of cavitation

through the small valve passages. The fluid is then drawn into

the piston cylinders (4) on the suction stroke and positively

displaced at the outlet at high pressure (5).

Drive Shaft

Shaft

Rotating

Disks

Inlet

Outlet

Suction

Section

Discharge

Section

Impeller

Section

Figure 1 The innovative TurboPiston Pump (TPP)

SHAFT

IMPELLER

ROTATING

DISK

Figure 2 Impeller and the rotor at the suction side of the TurboPiston pump.

The rotating motion harnesses the feature of a high volume

flow rate of the centrifugal pump (Turbo-motion); the piston

motion achieves the positive displacement feature of high

compression ratio of a piston pump, and the wedge volume

simulates the energy saving feature of the extended surface of a

rotary screw pump. The TPP is economical to maintain because

it has less moving parts than traditional reciprocating pumps. In

addition, a normal reciprocating pump requires a charge pump

upstream to assure proper chamber filling to avoid cavitation,

which can damage the pump or render the pump useless. The

TPP requires no upstream charge pump since the rotary motion

acts as its own charge pump. Due to its high rotating speed, the

TPP discharge is smooth and comparable to the centrifugal

pump. TPP displaces a fixed quantity of fluid per revolution like

a piston pump; thus, fine control of the flow rate is as simple as

controlling the speed of the unit at a linearly proportional rate.

Flexible valves

Eight cylinder chambers

Eight piston heads

chambers

3 © 2019 by ASME

Present New Orleans pumps can move an average of

335,650 gallons of water per minute (or 750 cfs) and discharge

at 30 psi. With a similar 12 ft diameter cross-sectional area

running at 2400 rpm, the TPP can pump 722,860 gallons of

water per minute (or 1610 cfs) and discharge at 500 psi with a

potential to 1000 psi with one stage. In this capacity, it could lift

a water column 2,300 feet high and transport water horizontally

for sixty miles. This would allow the flood waters to be moved

away in closed piping systems protected from overflow or

breaching. A single TPP pump, if successfully developed, could

pump flood water from anywhere in the Greater New Orleans

directly into the Mississippi River, Lake Pontchartrain, or the

Gulf of Mexico, some 40 miles away. This was the motivation

then, although the need for TTP is not there now because the

Army Corps has redesigned and constructed new flood control

gates and pumping stations surrounding New Orleans,

development of TTP continues because its unique characteristics

and potential broad applications. Table 1 lists the TPP's flow

rates corresponding to different sizes and rpms.

Table 1 Flow rates of various sizes of TPP

1.2 Comparison with conventional pumps

The concept of TTP was derived from the conventional axial

piston pumps designs [2]. In axial piston pumps (Fig. 3) the

cylinders and the drive shaft are parallel.

Figure 3 Axial Piston Pump [2]

The reciprocating motion is created by a cam plate, also

known as a wobble plate, tilting plate, or swash

plate. This plate lies in a plane that cuts across the centerline of

the drive shaft and cylinder barrel. The plate does not rotate. In

a fixed-displacement pump, the cam plate is rigidly mounted in a

position that intersects the centerline of the cylinder barrel at an

angle approximately 25 degrees from perpendicular. Variable-

delivery axial piston pumps are designed so the angle the cam

plate makes is perpendicular to the centerline of the cylinder

barrel and may vary from zero to 20 or 25 degrees to one or both

sides. One end of each piston rod is held in contact with the cam

plate as the cylinder block. The piston assembly rotates with the

drive shaft. This causes the pistons to reciprocate within the

cylinders. The length of the piston stroke is proportional to the

angle that the cam plate is set from the perpendicular

line to the centerline of the cylinder barrel.

Further characteristics can be found in Pump Handbook [3]

The major differences between the TPP and conventional axial

piston pumps are (a) TPP doesn't have the complex linkage

system and the cam plate and (b) TPP has more spacious and

efficient inlet and outlet flow chambers.

A comparison of the TPP specifications to those of other

common pumps can be seen in Fig. 4.

(a)

(b)

(c)

Figure 4 Comparison between TPP and conventional pumps with similar flow rates of approximately 650 GPM. (a) Weight Comparison (b) Pressure Comparison, and (c) Volumetric Footprint Comparison. Note: No single-stage centrifugal or gear pump is available for comparison at 1000 psi.

Since the TPP has not been fully commercialized, the

objectives of this study are:

(a) Using computational fluid dynamics (CFD) to gain further

understanding of flow behavior inside the pump.

(b) Estimating the total pressure losses in the flow path.

Piston

circle

(in)

Bore

(in)

Strok

e (in)

Flow Rate(USGPM) Flow Rate (ft3/s)

900 rpm 3600 rpm 900

rpm 3600 rpm

72 22.125 7.50 90,358 361,431 201 805

144 44.250 15.00 722,863

2,891,452 1,610 6,442

180 55.375 18.75 1,415,304 5,660,136 3,163 12,610

300 92.250 31.25 6,645,170 26,180,679 14,582 58,327

4 © 2019 by ASME

(c) Examining the potential cavitation locations under various

rotation speeds.

(d) Using the CFD results to guide design and manufacturing of

a TPP prototype.

2 COMPUTATIONAL ANALYSIS

This section introduces the computational scheme and the

steps involved in building the computational flow volume and

the methodologies used to simulate the flow field in TPP. The

commercial package GAMBIT is used to create the geometry

and construct the grids. The dimensions for this geometry are

obtained from the AutoCAD drawings. The commercial

computational Fluid Dynamics (CFD) software package

Ansys/Fluent (Version on 6.2.16) [4] is adopted for this study.

The governing equations are discretized using the control-

volume method [5]. The governing equations are solved

sequentially (not coupled) in the segregated solution method,

which employs an implicit pressure-correction scheme: SIMPLE

[5] algorithm. Second order upwind scheme is selected for

spatial discretization of the convective terms and species. The

non-linear governing equations are linearized implicitly and

these equations are solved simultaneously.

2.1 Governing Equations

The governing equations include the conservation of mass,

conservation of momentum and conservation of energy as shown

below. The continuity is described as

mSt

v.

(1)

The source Sm is the mass added to the continuous phase.

The momentum equation is presented in the Navier-Stokes

form,

Fgpt

.vv.v (2)

Where p is the static pressure, is the stress tensor; g

and F are the gravitational body force and external body forces.

In this study, the rotational motion is added as the body force.

No buoyancy force is considered.

The stress tensor is given by

v.I.

3

2vv T

(3)

Where is the molecular viscosity, I is the unit tensor, and

the second term on the right hand side is the effect of volume

dilatation.

In this study, the flow in the rotating frame of reference is

rotating with the speed of the shaft. The absolute velocity is

more efficient to use here. The calculation domain is divided

into several sub-domains with each rotating or translating. The

governing equations in each domain are written with respect to

that domain’s reference. The stationary flow domain is governed

by standard continuity and Navier-Stokes equations (not shown).

In the rotating domains, the continuity and the momentum

equations are solved in the rotating frame of reference. Here the

acceleration of the fluid is augmented by additional terms that

appear in the momentum equations. The rotating frame problems

are solved using the relative velocities or the absolute velocities.

The relative and absolute velocities on the rotating frame are

related as,

)(-vvr r

(4)

Where, is the angular velocity vector and r is the

position vector in the rotating reference frame. In an inertial

frame of reference, the left hand side of the momentum equation

is given as

)vv.(v

t (5)

For a rotating reference frame, the left hand side written in terms

of the absolute velocities becomes

vvv.v r

t (6)

In terms of relative velocities the left hand side equation is

given by

rt

rt

rrr v2vv.v (7)

2.2 Computational Model The simulation is conducted by separating the pump into

three separated computational domains: the suction section, the

discharging section, and the cylinder. The suction and

discharging sections are simulated using computational fluid

dynamics (CFD), whereas the compression process in the

cylinder is a straightforward pipe flow, so it is not simulated

computationally to safe the computational time. The total

pressure loss in the cylinder is calculated by an engineering

approach as a pipe flow. The dimension of the pump is

approximately 26 inches 17 inches 19 inches as shown in Fig.

5.

Figure 5 Selected dimension of the studied TPP

Figure 5 shows the actual pump casings and components. In

the computational domains, only the flow path is considered.

Figures 6 and 7 show the computational domains of the suction

and discharge sections, respectively.

5 © 2019 by ASME

Stationary

zone

Flow path

between impellers Rotating

zone

Figure 6 Computational domain of the suction section consisting of a stationary and a moving domain

Moving Zone

Stationary

Zone

Inlet

Figure 7 Computational domain of the discharging section consisting of a stationary and a moving domain

2.3 Boundary Conditions

The following are the boundary conditions considered for

each computational domain.

(a) Boundary conditions in the suction section:

The speed of the shaft equals 0 and 100 rpm. This

condition is imposed on the shaft wall as 2r (rpm),

where r = 1.37 inches is the shaft radius.

Mass flow rate at the inlet =1.337 Kg/s corresponding

to the shaft speed 100 rpm.

No slip condition at the stationary walls: u = v = w = 0

Pressure at the outlet varies with the location:

In the upper half of the circle (270o0o90o), valves

open.

P = -0.999999 atm gauge (or 0.000001atm absolute)

and a loss coefficient of 1.0 is assigned.

In the lower half of the circle (90o180o270o),

valves closed; the outlets are treated as walls.

Inlet turbulent intensity = 10 percent

Inlet turbulent viscosity = 10 kg/m-s

Operating pressure = 1atm

(b) Boundary conditions at the discharge section

Inlet condition:

In the upper half of the circle (270o0o90o), valves

closed. The inlets are treated as the wall.

In the lower half of the circle (90o180o270o),

valves open. The mass flow rate at the inlet is1.337

kg/s corresponding to the shaft speed of 100 rpm

Outlet boundary condition: pressure at 500 psig (34 atm)

The boundary conditions are assigned in GAMBIT. The

mass flow rate condition is assigned at the inlet face. The outlet

is defined as the vent outlet to include the pressure drop caused

by the piston valves in the actual device. The suction condition

at the outlet is assigned as an almost absolute zero, -0.999999

atm. In the actual operating condition, this outlet pressure

continues to change and increases as the water fills the cylinder.

However, since the transient condition inside the cylinder is not

simulated in this study, the initial suction value (a constant value)

is used for simplification during the entire simulation. After the

solution is obtained, a static pressure difference is added back to

the entire computational domain to compensate for the increased

outlet pressure value. This pressure difference is calculated by

assuming the total pressure at the inlet is 1 atm, which cannot be

doubly assigned when the mass flow rate is already assigned as

the inlet condition. This practice is justified because the

computational process only involves the pressure difference, and

the actual pressure values are not important for incompressible

flow such as water in this study. The loss coefficient is assigned

as “1.0” for the vent condition at the outlets. All the outer

surfaces are defined as walls with a no-slip condition on the

surface.

For each rotation of the impeller, discharge occurs 50% of

the time through only four cylinders because of the unique

design of the rotating disks. Each cylinder will experience

compression (discharge) and suction (charge) alternatively each

at 50% of the cycle. This feature of the pump could be

accurately simulated only in the transient model by

incorporating a specific program via the avenue of a User

Defined Function (UDF). Pressure at the outlet varies with the

location.

2.4 Turbulence Model

In this study, the standard k- model is employed. The

standard values of model constants are used without any

modification. Turbulent flows are significantly affected by the

presence of the walls. In this study, flows are partially driven by

wall rotation. The motion of the wall tends to impart a forced

vortex motion to the fluid by imposing a constant angular

velocity. An important characteristic of such flows is the

tendency of fluid with high angular momentum, which is the

flow near the wall, to be flung radially outward. This is often

referred to as "radial pumping'' due to the rotating wall pumping

the fluid radially outward. Since the near-wall motion is close to

solid rotation and the complex geometry in this study, the

standard turbulence wall function is used. In this approach, the

viscous sub-layer where the solution variables change most

rapidly is not resolved by the computational method. Rather the

near-wall velocity profile is assumed following the standard

laws-of–the-wall for mean velocity as described in

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ANSYS/Fluent manual [4]. The typical y+ value for the first

near-wall cell varies from around 80 in the narrow cylinder

passages to about 200 in the larger suction and discharge

chambers. Since the main purpose of this study is to use CFD

result as an engineering tool to provide a global flow and

pressure fields to guide design of the first TPP, this approach of

using the standard wall functions is deemed sufficient for this

industrial application.

2.5 Initialize Solution:

This is the initial guess provided for solving the governing

equations. The initial condition used is the inlet velocity -

0.2187462 m/s, which is opposite to the X-direction. Once the

solution is initialized, the convergence criterion is fixed, and the

solution is obtained by iteration.

2.6 Solution Methodology

The actual process of the periodic opening of charging

valves is simplified by inserting a stationary "shadow zone"

(shown in Fig. 8) covering the top half circle with a very thin

volume to receive the flow coming out of the four cylindrical

outlets from the charging section. This shadow zone consists of a

semi-circular section with the height equaling to the diameter of

the exit cylinder passage and a thin thickness of 0.28 inches that

is 10% of the piston cylinder passage length. The semi-circular

section is aligned with the upper half circle (270o-0o-90o) with

four discharge piston cylinders creating an interface between the

moving cylinders and the discharge pressure outlet condition.

The semi-circular section is assigned as a fluid zone but

stationary. The inlet surface of the semi-circular section forms

an interface with the moving domain, and the opposite surface

(the outlet surface) is assigned as the constant pressure outlet.

The other four faces of the domain act as walls. The domain is

meshed with 69,790 tetrahedral elements.

.

Inlet

Stationary

Shadow Zone

8 Moving Outlets

Figure 8 Solid mesh model for the charging section implemented with a stationary shadow zone

The domain is simulated for a transient flow, and a suitable

time-step is assigned based on the stability criterion by

examining the Courant number, Δt/ (Δxcell/ Ufluid). To avoid

instabilities the Courant number should be less than 1. To satisfy

this requirement, the maximum allowable time step to avoid

instability is 0.008 seconds for the 100 rpm case in this study.

One cycle time period is calculated as 0.6 seconds for 100 rpm.

The initial time step is taken as 0.001 seconds. Simulations are

carried out using 600 time steps with 50 iterations per time step

2.7 Creation Of Computational Flow Volume

Creation of the computational flow volume is not trivial.

The details for the extraction of the computational domain of the

section end are explained below.

2.7.1 Meshing the domain:

Because of the complexity of the geometry, Tetrahedral

mesh is used. Details of meshing in each computational domains

are described below.

2.7.2 Creating the flow domain passing through the impeller:

The 2-D face of the impeller profile is created in GAMBIT

using the vertices obtained from AutoCAD drawings. Edges are

created using these vertices followed by faces. The solid model

of the impeller hub is created using the “revolve” option in

GAMBIT. The 2-D blade profile is properly aligned on the vane

geometry, and the solid geometry of the blade is created using

the command “sweep faces”. The 3-D blade geometry is

extended beyond the actual height and then the “split geometry”

command is used to split the extended blade geometry from the

impeller hub. The computational domain of the flow passage

between the impeller blades is thus created. This computational

domain is then aligned with the “L” pipe using the split

command. More details of the process are explained in

Appendix D of [6]. The impeller section is also meshed using a

tetrahedral meshing scheme with the total number of 37,430

elements, as shown in Figure 9.

Figure 9 Tetrahedral mesh of the 3-D flow volume passing through the impeller.

2.7.3 Outlet domain:

The outlet section consists of eight cylindrical passages

through which water flows into the piston cylinder cavity. The

dimensions of the cylinders are obtained from the AutoCAD

drawings. A total of eight cylindrical passages are created and

joined with the vane flow volume. All the eight cylinders are

meshed using the “cooper mesh scheme” as shown in Fig. 10.

The Cooper meshing scheme is a structured mesh in which the

volume meshing is done by first meshing the edges and then the

faces. The meshing for the whole volume is then obtained by

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selecting these sources and sweeping these surface meshes

through the entire volume. The total number of meshed elements

is 21,808 in the outlet passages. The total number of the meshed

elements for the entire suction section is 60,220 as shown in Fig.

10.

OUTLETS

Figure 10 Tetrahedral meshes of the 3-D solid model of the outlet cylindrical passages.

2.7.4 Compressing cylinder:

The reciprocating flow motion inside the compressing

cylinder is a straightforward pipe flow, so it is not modeled to

save computational time. The total pressure losses in the

compressing cylinder are computed using engineering internal

flow correlations.

2.7.5 Discharge section:

Figure 11 shows the 3-D solid model for transient discharge

section. The same technique of using a stationary "shadow zone"

to interface the rotating domain for the transient inlet condition

is applied at the bottom half of the circle. A total number of

67,956 tetrahedral elements are meshed in this domain.

Inlet

Outlet

Figure 11 Tetrahedral meshes of the discharge section with a stationary shadow zone.

2.8 Convergence Criterion

In this study, the convergence criterion of 10-3 is chosen for

the residuals of continuity (mass conservation), 10-6 for velocity,

turbulence kinetic energy “κ” and dissipation rate “ε” for the

stationary and moving reference frame, and 10-5 for the transient

case.

2.9 Grid Sensitive Study

A representative grid sensitivity is presented in Table 2 with

the number of elements equal to 60,220 against 183,735

elements at the suction end. Since the mass flow rate based on

the RPM is assigned as the inlet condition and the exit is

modeled as a shadow zone connecting to the discharge section

and is subject to transient opening or closing of the valves, the

pressures in the inlet and outlet are calculated by CFD and are

hereby monitored for grid sensitivity study. As shown in Table

2, the pressure difference between the two grids are 0.0087% at

the inlet and 0.0014% at the exit respectively. To further assess

the grid sensitivity study result, the difference of the total

pressure losses from the inlet to the exit between these two grids

is compared and shown a difference of 5.61% in Table 2.

Considering the nature of this study as a first step toward

providing a preliminary view of the complex flow inside a new

pump, the results of using 183,735 elements for the suction side

is accepted without proceeding to the employment of finer

meshes. A similar process is employed in the other

computational domains.

Table 2 A representative grid sensitive study

Domain Meshed

Elements

Ptot at inlet

(atm)

Ptot at outlet

(atm)

ΔPtot 1-2

(atm)

60,220 -0.9973215 -0.9990247 0.0017032

183,735 -0.9972345 -0.99903886 0.00180436

DP between two grids (%) -0.0087 0.0014 5.61

Suction

3 RESULTS AND DISCUSSIONS

A rotational speed of 100 rpm is simulated. The time period

is computed using T = θ/Ώ, where “θ” is the sector angle in

radians, and “Ώ” is the rotor speed in radians/sec. Using the

above expression, one cycle time period is calculated as 0.6

seconds for 100 rpm. The time step is taken as 0.001 seconds.

Simulations are carried out using 600 time steps with 50

iterations per time step.

3.1 Suction Section - Sliding Mesh Transient Case

The transient model of Fig. 12 shows the sector angle and

the direction of rotation looking against flow direction from the

disk toward the flow inlet.

θ=0o

Ώ=100rpm

θ=450

314?

θ=2400

Figure 12 100 rpm, Transient Case: Transient model showing the sector angle and the direction of rotation looking against flow direction from the disk toward the flow inlet.

8 © 2019 by ASME

3.2 Suction Section at θ = 2400

The instantaneous snapshot of the flow phenomenon

exhibits recirculation losses occurring at the elbow as shown in

Fig. 13.

Recirculation zone

(a)Total pressure at y-midplane (b)Total pressure at x-midplane

(c) Static pressure at y-midplane (d) Static pressure at y-midplane

Figure 13 Instantaneous contour plots of the total and static pressures (atm) with the velocity (m/s) vectors at the x- and y-midplanes of the “L” shaped pipe at θ = 240

0.

Figure 14 Instantaneous contour plot of the total pressure (atm) with the velocity (m/s) vectors at a plane across the impeller at θ = 240

0.

The regions of relatively high total pressure losses in Fig. 14

follow the rotating motion of the open pistons in the upper half

region with open outlets than the lower half without outlets.

Figure 15 shows the contour plot of the total pressure across

different section-planes of the impeller to illustrate a flow path

that generates large total pressure losses, which are shown to

extend through the whole length of the impeller.

1

2

3

Figure 15 Instantaneous contour plot of the total pressure (atm) at four different impeller planes at θ = 240

0

wall

outlet

Figure 16 Instantaneous contour plot of the total pressure (atm) with the absolute velocity (m/s) vectors at the outlet walls (for closed cylinders) and outlet plane (for open cylinders) at θ = 240

0

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At the exit surface of the "shadow zone,” the effect of the

lateral diffusion is minimal as evidenced from the velocity

distribution at the exit in Fig. 16. This negligible lateral diffusion

justifies the method of adopting a "shadow zone" to simplify the

dynamic boundary condition for the sliding mesh condition.

3.3 Suction Section at instants ( θ = 300 and 300

0)

Since there is not much significant difference in the flow

patterns between 240o and 30o or 300o (although their

magnitudes are different), the detailed figures are not shown

here, but they are documented in [6]. The total pressure loss is

slightly more at θ = 300 than at θ = 3000. The regions of low

static pressure are larger at θ = 300 than at θ = 3000 as can be

seen from “A” and “B” in Fig. 17(a) and (b). These areas of

significant low pressure could create cavitation as the rotational

speed increases.

A

(a)

B

(b)

Figure 17 Instantaneous static pressure (atm) contour plots across the midspan of the impeller (a) θ = 30

0 and (b) θ = 300

0.

3.4 Discharge Section at θ = 600

The flow pattern and total pressure distribution in the

discharge section are shown in Fig. 18. The circled regions

indicate the maximum total pressure just after the flow enters the

inlets of the discharge section in the bottom cylinders and the

large total pressure losses in the elbow. At θ = 2100, Fig. 19

shows regions of maximum total pressure “B” and minimum

pressure “A”. Again, the overall flow is highly complex and 3-

D, which creates a lot of entropy.

Plane 1

Plane 2

Figure 18 Instantaneous total pressure (psi) contour plot with velocity (m/s) vectors at two different planes parallel to the disk at θ = 60

0.

The transient computation shows regions of more

pronounced maximum total pressure “B” and minimum pressure

“A” in Fig. 19 just after the flow enters the discharge section at θ

= 1200. Figure 20 shows the flow pattern on a horizontal (z)

plane for flow entering from cylinders to the discharge section.

In Fig. 21 the total pressure contour plot with the velocity

vectors shows multiple re-circulation regions in the discharge

section. In addition, these are multiple recirculations and

whirlpools in other regions not shown in figures are sources for

generating entropy, resulting in total pressure losses.

A B

Figure 19 Instantaneous contour plot of the total pressure (psi) with the velocity (m/s) vectors after the inlet at θ = 210

0.

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Inlet Inlet

Figure 20 Total pressure (psi) contour plot with the velocity (m/s) vectors in a horizontal (z) plane across the inlet to the discharge section.

3.5 Total pressure losses and pump performance

Only frictional losses created by fluid mechanics are

considered in this study without considering the other

mechanical losses due to seals and rotating shafts. The total

fluid mechanical losses in the TPP are calculated by adding the

total pressure losses from the suction domain, the piston-cylinder

sections, and the discharge domain. The total pressure losses in

the cylinders are calculated using engineering calculations as a

pipe flow. Table 3 lists the total pressure losses of each section

and the calculated loss in efficiency of the TurboPiston pump at

each cylinder position. The results show the average total fluid

mechanical losses are about 0.02% at 100 rpm for a pump head

of 34 atm (500 psia) simulated in this study. This small loss is

due to a low flow rate of 100 rpm. If the total pressure loss is

assumed to be proportional to (rpm)2, the average total pressure

loss is about 27% (or hydraulic efficiency of 73%) for 3600 rpm

with a pump head of 34 atm. The above assumption although is

an oversimplification because the TPP possesses the hybrid

characteristics of both centrifugal and piston pumps. The true

pump performance and efficiency will need to be obtained from

experiments.

Figure 21 Total pressure (psi) contour plot with the velocity (m/s) vectors showing different recirculation regions in the discharge section.

Table 3 Total pressure losses and efficiency losses of TPP based on 100 rpm calculated in this study and estimated

losses for 3600 rpm.

Time

(sec)

Cylinder

Position

(deg)

Loss,Suction

(atm)

Loss,

Cylinder

(atm)

Loss,

Discharge

(atm)

Total

losses

(atm)

Efficiency

loss (%) at

100 rpm

Estimated

efficienicy

loss (%) at

3600 rpm *

0.050 300 0.002332 0.000850 0.001482 0.004664 0.0141 18.32

0.100 330 0.002616 0.000850 0.001766 0.005232 0.0159 20.55

0.125 345 0.002606 0.000850 0.001757 0.005212 0.0158 20.47

0.150 360 0.003026 0.000850 0.002176 0.006052 0.0183 23.77

0.200 30 0.003199 0.000850 0.002349 0.006398 0.0194 25.13

0.225 45 0.003537 0.000850 0.002688 0.007075 0.0214 27.78

0.250 60 0.003610 0.000850 0.002760 0.007220 0.0219 28.35

0.300 90 0.003935 0.000850 0.003085 0.007870 0.0238 30.91

0.350 120 0.003929 0.000850 0.003079 0.007858 0.0238 30.86

0.450 180 0.004463 0.000850 0.003614 0.008926 0.0270 35.06

0.55 240 0.004619 0.000850 0.003769 0.009237 0.0280 36.28

Average 0.003443 0.000850 0.002593 0.006886 0.0209 27.04 * The estimated loss for 3600rpm is based on the assumption that the total pressure loss is proportional to (rpm)2.

11 © 2019 by ASME

4 CONCLUSIONS

A 3-D computational model has been constructed for

the newly developed TurboPiston pump. The commercial

CFD code, ANSYS/Fluent, was used to solve the complete

3-D Navier-Stokes equations to obtain the flow field and

the total pressure losses. The standard k- turbulence

model was used. Rotation speed at 100 rpm and pump

pressure of 33 atm was computed. The results are

summarized below.

Total pressure losses vary with different positions of

the rotation angle and from moment to moment. Total

pressure losses are found in the entrance duct, the stagnant

region near the outer 90-degree bend and the separated

region downstream of the inner 90-degree bend. Areas of

significantly low static pressure occur in the flow passages

through the impeller and downstream of the inner 90-

degree bend of the entrance duct. Since cavitation may

occur in these areas of low static pressure, experiments are

needed to help identify whether or not cavitation occurs.

Redesign of the entrance duct and the impeller vanes could

minimize or alleviate the cavitation problem.

The total pressure losses for 100 rpm are minimal,

approximately 0.02% of the pressure (34 atm) produced by

the pump. However, if rpm increases to 3600, the average

total pressure loss is estimated to be about 27% (or

hydraulic efficiency of 73%) based on the simple

assumption that the total pressure loss is proportional to

(rpm)2.

4.1 Future Work

Guided by the result of this CFD study, the

following future work is considered:

Use 10 times more finer meshes.

Incorporate the cylinder dynamics into the

computational domain.

Redesign the entrance duct elbow and the impeller

vane geometry to reduce the total pressure losses.

Redesign the discharge section flow path to reduce the

total pressure losses.

Fine tune the geometry of the impeller.

5 ACKNOWLEDGEMENT

This study was supported by a grant from the

Louisiana Board Regent's Industrial Tie Research

Subprogram. The authors want to thank Ms. Kiranmayi V.

Sristy for performing the CFD analysis.

6 REFERENCES

1. "Wood Screw Pump,"

https://en.wikipedia.org/wiki/Wood_Screw_Pump

2. Axial Piston Pump

http://hetacfluidpower.com/images/screen_shots/Pisto

n2.jpg , 2015

3. Karassik, I. J., Pump Hand Book, McGrawHill, 1985,

ISBN 007033325.

4. ANSYS/FLUENT User’s Guide, 2019

5. Patankar, S.V., Numerical Heat Transfer and Fluid

Flow, McGraw Hill, 1980.

6. Sristy, K. and Wang, T., " Analysis of a TurboPiston

Pump,” ECCC Report 2006-03, Energy Conversion

and Conservation Center, University of New Orleans,

August 2006.

12 © 2019 by ASME

Appendix A Manufacturing of a 12-inch Plastic Model and a metal prototype of TurboPiston Pump

Based on the results of CFD analysis, a 12" diameter plastic

demonstration pump was fabricated. To allow detailed

examination and visualization of the working principle of TPP,

cranking handled is installed instead of a pump. Also a 12"

metal pump prototype was manufactured. Selected parts are

shown in the following photos.

Figure A1 The 12" plastic demonstration TPP.

13 © 2019 by ASME

Figure A2 Selected parts of the 12" metal prototype of TPP