For cost considerations, the reversible pump-turbine is the right choice for pumped storage schemes. The present trend is to build pump-turbines for higher heads and large capacities machines of 600m head (single stage) and capacity per unit as high as 300MW are already in operation[1], while machines of 800m head (single stage) are reported to be in advanced stage of installation.

The data given for such plant are, the discharge values corresponding to the maximum, rated and lowest heads for pump mode, and the rated and overload power output during turbine mode, at some given heads. The basic issue is to study the considerations in the hydrodynamic design process, which would yield an impeller with blades that are hydro-dynamically efficient, easy to manufacture and mechanically sound to give a trouble-free range of operation.

During the planning stage, the usual question that may be raised is whether we can adopt, as such, any of the existing designs with a range of parameters near about the required range of given requirements or should a fresh design be embarked upon? The purpose of this paper, in the above context, is to discuss a hydrodynamic design procedure for achieving the specified hydraulic characteristics and also simultaneously satisfying the stress considerations by a judicious choice of certain variables.

A project had been taken-up to develop a reversible pump-turbine with the intention of developing this capability, keeping in mind the future needs of the country. The author designed a pump-turbine impeller by a hydrodynamic method and its performance characteristics were predicted, by flow analysis both in pump and turbine modes[2]. This work was done from first principles with total in-house effort.

Subsequently, a homologous model was manufactured and its performance testing was done at the Hydroturbine Laboratory at BHEL-Bhopal, in order to validate and prove the reliability of the design and flow analysis procedure. The test results are available in a report[8]. This paper brings out the hydrodynamic design and performance prediction method for a reversible pump-turbine impeller.

Hydraulic design considerations

The preliminary parameters such as the speed of rotation and the impeller diameter can be determined on the basis of statistical data of the known units in operation[3], [4]. In fact, the speed of rotation is selected on the basis of turbine ratings, while the maximum diameter of the impeller is chosen from pump consideration, suitably for the ratio of maximum and rated pump heads. The main task is to ensure that the unit that is proposed for the plant shall have the Head-Discharge (H*-Q*) characteristics in pump mode as close as possible to those given.

H* and Q* are head and discharge parameters in normalised form incorporating a reference diameter of the impeller, D1, speed of rotation, n, discharge through the impeller, Q, and head, H. A single plot of available values of H* and Q* of various pumps under study helps to make a useful comparison amongst them in the range of their trouble free operations. The values at end points and the slope of H*-Q* line would serve as valuable data as a guide for a new development.

To take advantage of some available developments for their direct application, a comparative study of the achieved and required characteristics on a single plot – H*-Q* in pump mode has been shown (Fig.1) and a plot of Q11-n11 in turbine mode may also be made. For better comparison, different combinations of speed of rotation and impeller diameter may be tried. If they show good agreement, the available development may be used. However, experience has shown that in most cases such applicability is seldom found. The reasons being either that:

• in pump mode, the slope of H*-Q* characteristic is found to be quite different from that required, or the maximum-head operation point falls in the unstable zone of operation in respect of the available developments, or

• in turbine mode, the minimum head of operation falls very much away from the best efficiency point.

Such a situation leads us to design a unique pump-turbine – at least the impeller blade profile – for the required parameters.

The pump-turbine impeller is designed as a pump[5], [6] from hydrodynamic considerations. The success of design depends on its pump-mode operation. Therefore, the crucial parameters like the design head and corresponding discharge have to be carefully selected in relation to the maximum head and its corresponding discharge. It would always be advantageous to push the unstable zone towards lower discharge by keeping the design head nearer to the maximum head. Further, at the planning stage, the maximum head of pump should be kept just below the lowest point of the hump, which is a characteristic of mixed flow pump, on the H*-Q* characteristics, with due margin to allow for permissible grid frequency variation. Typically, discharge at its best efficiency point, should be 1.087 to 1.11 times the discharge corresponding to maximum head.

We may appreciate the intricacy of design when we look at performance results of a pump-impeller and a turbine–runner placed back-to-back, as shown, in the Fig.2, we observe the following. On these characteristics best efficiency points and the lines of maximum, minimum and rated head lines are shown.

On the turbine performance characteristic, the output limiting line and the point at which rated power at rated head is available has been shown. There is a zone of its rough behaviour, which is on the left of output limiting line. The turbine may run into this zone when called upon to operate at part-loads at rated head and at low heads to achieve higher power. On the pump performance characteristic, the H* – Q* curve has a hump which is a zone of unstable behaviour for the pump when it is pushed to operate at higher head. Operations in rough zone of turbine and unstable zone of pump are associated with undesirable noise and excessive vibrations. Thus, the operating parameters should be away from these zones.

In other words, the operating parameters of an new development during design should be so chosen that on the derived performance characteristics from the laboratory test, that they do not fall in these zones. This aspect is very important to be in due consideration when a development of a pump-turbine impeller is undertaken. Where an impeller of a pump-turbine is designed, primarily, as a pump to lift water from lower reservoir to higher reservoir and is accepted as such, for it to be used as turbine–runner to generate power studies have shown that the turbine characteristics shift from the desired value towards lower flow rate (Q11) and low speed (n11). This would mean that rated power point lies on the left of the output–limiting line of the shifted characteristics (shown by dotted lines) in the turbine mode, where efficiency value is lower, as a consequence available power would be less. In an obvious attempt to achieve the rated power by increasing guide vane opening, the machine would be pushed to operate further away from the unacceptable output–limiting line and would be in the rough zone of performance.

Therefore, an appropriate measure has to be taken at the beginning of the impeller design so that shifting of turbine is restricted and is held at the desired location and its pattern of characteristics is preserved. The key point is that an adequate quantity of flow rate should pass through the impeller in turbine mode at the rated point.

We know that analytically, during pump operation, the H*-Q* relationship is linear and is expressed as:

And, the slope of the line is:

Where,

β1 is the blade angle at the impeller outlet and α2 is the absolute flow angle at the impeller inlet in pump mode.

The satisfactory operation would depend upon the slope for a specific requirement. Near the best efficiency point of operation, the water entry to the pump is nearly axial, i.e. a2 = 90°. Then the slope of H*-Q* curve shall depend on the slip factor m, on the hydraulic efficiency hh, on the ratio D1/ b1 and on the angle b1. To cater to a large head variation, the H*-Q* curve should have a steep slope. It is evident that the required value of slope can be achieved by proper selection of these parameters. Of these, the role of m and b1 is significant. The magnitude of b1 has to be estimated correctly in advance, otherwise the pump will not deliver the required discharge at desired head.

Further, the success of the design depends on the achievability of the rated output at design head at a reasonably high value of efficiency in turbine mode. Generally, as mentioned before, the impeller is designed principally as a pump and results of model tests in turbine are accepted as such. In the authors’ opinion, in some cases, the objective of delivering the rated power in turbine may not be achieved. To ensure the generation of rated output of the turbine, the blade angle at pump inlet, which will control the discharge during turbine operation, has to be suitably calculated. In other words, the pump’s outlet angle should be calculated from pump considerations, while its inlet angle from turbine considerations corresponding to the best efficiency point. These considerations have been the main focus in the development of the impeller design.

**Impeller blade design**

The design of impeller blade profile should satisfy the following requirements:

• The impeller should provide an acceptable distribution of relative velocity on both pressure and suction sides of the blades, in order to minimise the possibility of flow separation and the accompanying loss in performance.

• The evolved blade surface should be such that it can be manufactured accurately by means of automated fabrication procedures.

• The blades should be designed so as to keep the stresses at a safe level, eliminating the possibility of occurrence of excessive distortion or fracture during operation.

A hydrodynamic design procedure of blade profile is preceded by selection of contours of band and crown, of guide vane passage height, and of leading and trailing edge geometry which make the runner space in 3-dimensions. The design is a part of quasi three-dimensional flow analysis achieved as a combination of two bi-dimensional flows in the meridional plane from band to crown and between blade to blade surfaces.

The first step assumes the flow to be axisymmetric and involves determination of the meridional velocity on the stream surfaces, which divide the impeller/runner space into a number of thin filaments of varying thicknesses. The governing flow equation in terms of stream function may be solved by Rayleigh-Ritz approximation method for a given velocity distribution at inlet and outlet of the runner. The entire procedure of computation can be accomplished on a digital computer through the code MERD[7]. The output is the meridional coordinates (r, z) of a number of points along each streamline and the values of meridional velocity at these points.

The second step in the design proceeds on the streamlines found as a result of the first analysis. The distribution of angular momentum is calculated from the specified loading distribution:

Where,

Ws and Wp are the relative velocities on suction and pressure sides of the runner respectively, s is the meridional length of blade camber line and this combined with the meridional velocity distribution. Here, an appropriate loading distribution has been selected[2]:

and,

where,

ε is coefficient of restriction produced by a blade. The meridional component Vm and tangential component Vθ of the absolute velocity at a point is obtained by applying equation of continuity and condition of irrotationality in the region enclosed between the point in consideration and the inlet of the impeller vane:

and,

The skeleton line of the blade represents streameline of the relative flow. The inclination of the skeleton with the meriodinal direction is:

Sufficient information is then available to construct the velocity triangle and to evaluate the flow angle x at a computing point. Then, the relative velocity vector of blade camber could be traced as:

Where,

the blade circulation is:

and,

σ1 is length of meridional streamline from point 2 to point 1 and k is a constant ensuring a specified included angle at the center of runner between inlet and outlet known as plan angle in r-θ plane.

For a pump-turbine impeller, the rated flow rate in turbine mode is more than the rated flow rate in pump mode, this inequality exists at the best efficiency point as well. Further, the blade angle, the opening between the two consecutive vanes at their tips and the discharge through the impeller are closely related. At best efficiency point of operation, to establish QT > QP, the impeller blade angle b at point 2 should be larger than that would correspond to QP. Then, in order to achieve desired flow rate through the impeller, the exit blade angle as pump (point 1) should correspond to discharge at best efficiency as pump while the exit blade angle as turbine (point 2) should correspond to discharge at best efficiency as turbine. However, along each meridional streamline, the blade angle should smoothly vary from point 1 to point 2.

Considering these aspects a factor Q / QP at points along a meridional stream line starting from point 2 to point 1 has been used as :

Where,

QT is the discharge at the best efficiency point in the turbine mode. It is approximately equal to 0.86 times the rated discharge (based on studies on existing efficient developments), and QP is the discharge at the best efficiency point in pump mode.

In normal development practice, designers increase the openings between the blades at the turbine outlet (point 2) by manual manipulations to an extent that the required discharge is achieved during the model test corresponding to rated power of the prototype by a trial and error method. In some cases there could be four or five such trials; the entire process is quite time consuming. Instead, the sugested technique can ensure the required discharge in the turbine mode as blade angles are suitably computed in the outset.

The angular coordinate u of the blade at each point is obtained by integrating the calculated x-distribution, as follows:

In this integration, u is initialized to zero, i.e. taken as radial at the inlet edge for ease of fabrication, at s = s1, u is angular blade spread (plan angle) in r-u plane.

A suitable thickness distribution law is adopted, usually giving uniform thickness in the central portion and gradually decreasing towards the edges. The thickness at each point is evaluated by interpolation and applied at the local normal to the camber, in order to obtain points on both suction and pressure surfaces.This procedure is repeated for all the streamlines in the meridional plane of the runner from band to crown. In order to reduce the pressure fluctuations during pump and turbine operations, the runner blade at the edge of pump outlet may be kept at some inclination, say, at 20° from the vertical; such that the plan angle of the skirt profile is smaller than that at crown. The maximum value of the blade thickness is adopted from stress considerations. However, this has to be checked later by stress analysis. As a guide, the thickness (in mm) may be taken as (1.0-0.7) D1/HP for 100m-500m of pump head. Higher coefficients correspond to lower values of head.

The obtained points on the stream surfaces, when taken in order, generate the two pressure and suction surfaces of the blade. The entire computation scheme has been organised in a computer code PTNEW. During the computation, the number of computing points (51) both for suction and pressure sides has been taken equal for all the streamlines, so that, when identical points on the two surfaces are joined in transverse direction on all meridional stream surfaces, it results in a grid with rectangular topology. It helps in generating 3-D solid model of the blade through Solids Modeller, I-DEAS[9], and in using this mesh as such for Finite Element (FE) stress and vibration analysis of the blade through FE analysis package ANSYS[10]. The colour photograph of a single pump-turbine blade generated through Solids-Modeller using the designed 3-D coordinates on the pressure and suction surfaces, is shown in Fig. 3

### Performance prediction

Prediction of performance characteristics, both for pump and turbine modes, is done analytically to ensure the required performance of the machine. This calls for computing the hydraulic losses in the impeller, guide vanes, stay vanes, spiral-casing and draft-tube. The volumetric, disc friction and mechanical losses are computed separately. The efficiency is estimated after combining all these losses.

To estimate the losses in the impeller, the velocity field is calculated assuming a frictionless flow field in the designed impeller space from band to crown along the middle stream surface. The viscous effect is considered assuming boundary layer growth over the flow surfaces and the shear stress. The latter is evaluated using the analogy of flow in circular pipes, i.e., shear stress = l r W2/8, l being the friction coefficient for pipes for the same Reynolds number.

Energy losses due to skin friction, shock at inlet and mixing at outlet are considered. The same procedure is adopted for loss estimation at guide vanes and stay vanes. Friction losses at spiral casing are estimated using the pipe analogy, both for the pump and turbine modes of operation. The shock losses are added on, for operation at off-design points during pump mode of operation. While only friction losses occur in the leg, bend and cone of the draft-tube during pumping, additional losses due to expansion in the cone and leg portions and exit losses are also incurred during operation as turbine mode. The efficiency is calculated as follows:

For Pump Mode:

• The effective head developed by the machine is given by:

H_{p} = H_{th} – (h_{r} + h_{gv} + h_{st} + h_{sp} + h_{dt}) (5)

• The power input is given by:

P(kW) = 9.81 x Q x H_{th} + P_{d} (6)

Where, P_{d} is the power consumed by disk friction.

• The hydraulic efficiency is given by :

• The overall efficiency in pump mode is given by :

*For Turbine Mode:*

• The head on the machine is given by:

H_{T} = H_{th} + (h_{r} + h_{gv} + h_{sp} + h_{st} + h_{dt}) (9)

• The power output is given by:

P(kW) = 9.81 x Q x HT x h – Pd (10)

• The hydraulic efficiency is given by:

The variation of head, power and efficiency with discharge can thus be arrived at, for different guide vanes openings at the given speed in pump mode. Similarly, in turbine mode of operation, the variation of unit discharge and efficiency with unit speed, are generated[2]. The code used for loss calculation is LOSSES. Based on the computations, the Fig. 5 shows the components of loss values for the guide vane opening at the design condition in pump operation and corresponding values in turbine operation. The pump and turbine characteristics thus derived are shown in the Fig. 6.

### Model Testing

The prototype data are given below:

*As Pump*

Rated design head = 175.0m

Rated discharge = 88.05m3/s

Speed = 273rpm

Unit speed = 92.49rpm

H* = 116.89m, Q* = 3.59 m3/s

*As Turbine*

Rated output = 152.4MW

Rated head = 163.36m

Unit speed = 95.84rpm

*Main Dimensions*

Maximum runner diameter = 4482.0mm

Guide vane height = 555.0mm

Number of runner blades = 7

Spiral casing inlet diameter = 2980.0mm

The homologous model of this design was made with maximum runner diameter of 447mm. The blades, crown and band were made separately and assembled together by screwing/brazing. The band was made out of transparent PerspexTM material, to enable flow visualisation from outside. A colour photograph of this model runner is shown in Fig. 4. This model was tested for entire four quadrant operating range, for different guide vane openings at the test stand at Bharat Heavy Electricals Ltd., at Bhopal[8].

The flow rate through the model was measured by electromagnetic flow meter, calibrated using a weighing tank. The head measurement was carried out using pressure transducers, and torque measurement using torque transducers, while speed was measured using high precision proximity detectors. All the measured parameters were processed and analysed through a data acquisition system and a dedicated computer to give the results in print. The absolute model turbine efficiency is achievable within an accuracy of 0.25%. Depending on the type of test, the head on the model was suitably maintained but did not exceed 18m.

The following scale-up correction formula, based on iec 60193[11], was used to work out the prototype efficiency from the tested model efficiency corresponding to the maximum efficiency point:

Where, K has been taken as 0.7 for turbine mode and 0.6 for pump mode.

In pump mode, the test results show that the maximum efficiency of the model is 86.87% corresponding to unit speed of 92.54rpm and unit discharge of 324.88l/s, H* = 116.79m and Q* = 3.51m3/s. The H*-Q* values have been shown on the graph along with the prototype values predicted as a result of flow analysis. Prototype efficiency values are obtained by adding 4.09 to the model efficiency values, and it works out to 90.96%. The comparison of predicted and achieved values of H*-Q* and h-Q* for the prototype is shown in Fig. 7.

In turbine mode, the maximum model efficiency achieved was 86.03% at unit speed of 80.12rpm and unit discharge of 324.41l/s. The prototype turbine efficiency values have been obtained by adding 5.06 to the model efficiency values, and it works out to 91.1 %. The comparison of the theoretically predicted prototype values of Q11-n11 and h-n11 with those achieved by model tests and then scaled up for prototype is shown in Fig. 8 for a case when flow angle from the guide vane is 20.5°. Further at the best efficiency point, the ratio of turbine and pump unit discharges is 1.0 and that of unit speeds is 0.866.

It may be observed that the model performance characteristics in both pump and turbine modes for the prototype size are in reasonably good agreement with the predicted ones, which suggests that the design procedure evolved by the authors may serve as an effective tool in the development of reversible pump-turbine runners.

**Conclusion**

• An increase in efficiency can be achieved by improved designs not only of the runner but also of the guide vanes, the stay ring, the draft tube and of the spiral casing, by the above method;

• Leading edges of the runner must be carefully determined using a method based on theoretical flow calculations and the profile checking should be done using template made by computer graphics, in order to avoid any local defects which may lead to cavitation;

• The model test results show that a steeper head-discharge curve is required, and for achieving higher part-load efficiencies, the outlet vane angle b1 is reduced by increasing the guide vane passage height. By reducing the spiral inlet diameter, one may also achieve a steeper head-discharge curve.

• It has been observed that by increasing the discharge diameter by a small amount, say 0.5%, the increase in the maximum head limit is about 2.5% and the increase in the pump efficiency may be of 1.0%;

• Inlet edge cavitation on the suction side can also be suppressed by extending the inlet edge towards the suction end;

• The inlet edge cavitation can also be suppressed by improving the inlet edge profile by ensuring shock-less entry at the required regime of optimum operation. This is possible if the flow angle corresponding to shock-less entry is accurately determined during the experimental studies of the first variant of runner model;

• Stress analysis has been carried out on the prototype runner by FE using ANSYS. Maximum stress always results at the crown root. This has been found to be 2700kg/cm2 average stress with about 8% fluctuation, at runaway speed. Since the runner material is a special cast stainless steel with excellent yield (6000kg/cm2), tensile (7500kg/cm2) and fatigue (2600kg/cm2) stresses, the factor of safety is as high as 2 even at runaway speed of turbine; and,

• Any modification, which may be contemplated after model testing for improvement in the results, should be done in the design parameters once again and the design cycle should be repeated. In the authors’ opinion, two to three iterations may give the desired results.

### Acknowledgment

The authors wish to acknowledge the valuable assistance from all his colleagues who have been associated directly, and indirectly, in the above studies.

Adarsh Swaroop, Professor, Department of Civil Engineering, Lakshmi Narayan College of Technology, Bhopal India

S M Ramanathan, Senior Manager, BHEL, Bhopal, India