Cyclic Pressure Test of Vapour Core Pump of Reheat Fuel Control System of An Aero-Engine

Cyclic Pressure Test of Vapour Core Pump of Reheat Fuel Control System of An Aero-Engine

Arun Kumar Sc. D and Kamesh Goyal Sc F Regional Centre for Military Airworthiness, CEMILAC, HAL P.O., Lucknow-226016

Abstract

Airborne accessories and systems are required to successfully undergo a number of qualification tests as per airworthiness certification procedures before these can be fitted on the platform (aircraft/helicopter). Qualification tests and their severity level are governed by the mission /usage criticality, safety and their operating flight envelope. Cyclic pressure test is one of the very important test performed during qualification for evaluating the fatigue life of pressure vessels, which, in turn, is helpful in arriving at the useful life of the accessories/system.

For evaluating the design of the vapour core pump for cyclic pressure test, there are three cyclic pressure levels i.e. low pressure, intermediate pressure and high pressure are to be applied. But the design of the pump is such that three physically distinct zone cannot be created. Hence by an innovative approach i.e. Equivalent Pressure is calculated and applied to simulate the load arising on the pumps due to three cyclic pressure levels. For calculating the equivalent pressure, the whole pumps is theoretically divided in three pressure zone i.e. low pressure zone , intermediate pressure zone and high pressure zone. The addition of forces acting on three pressure zones gives the total force acting on pump casing. Equivalent Pressure is obtained by the total force divided by total area.

For creating the Equivalent Pressure in pump during testing the orifice size to be fitted at outlet of pump is calculated with the help of flow number at inlet and outlet of the pump.

Keywords: Cyclic Pressure, Equivalent Pressure, Vapour Core Pump and Flow Number

1. Introduction

   Fuel system LRUs are exposed to pressure pulsation during service life. Cyclic pressure test is carried out during qualification to emulate these

   pressure pulsations seen by the LRUs during service life (Cyclic Pressure test qualifies the product design). Added benefit of cyclic pressure testing is to determine weak link in the design.

   Crack initiation and propagation [1] are two important factors towards testing for fatigue. Crack initiation is not expected to take place before the end of useful life. Inherently, Fuel LRUs do have multiple stress raisers. It is the designers expertise and experience which governs the importance of a given stress raiser and design is concluded accordingly.

   To arrive at appropriate cyclic pressure test plan, cycle rate is decided based on usage of LRU and duration of cyclic pressure test is decided from S-N curve of the material [2].

   It is rather simpler to carry out cyclic pressure test on bodies of LRU having constant pressure along

   the line of flow like cylindrical bodies. But it becomes tedious when a body with varying geometry is to undergo cyclic pressure test as pressure is varying along the flow line. For example, in case of centrifugal pump, pressure will follow parabolic variations along the impeller blade due to its geometry. An approach for carrying out cyclic pressure test on vapour core pump is being explained below.

2. Vapour Core Pump

   Vapour Core Pump is one of the major sub- assemblies in a Reheat Fuel Control system. Reheat Fuel Control System[3] supplies fuel for augmenting the basic thrust of the engine during acceleration and take-off. This is achieved by providing metered fuel flow through reheat system in response to electrical signals from Digital Engine Control Unit (DECU) of the engine. Fuel flow from Filter passes through a plug in hole type flow meter and reaches Inlet Throttle Valve of the pump. Operation of Inlet Throttle Valve is, in turn, controlled by the DECU to set the desired pump outlet flow. Outlet of pump goes to the engine manifolds via a Transient Pressure Regulator (TPR). When Reheat is off, Inlet Throttle Valve [4] allows

   cooling flow through a hole in it and when reheat is selected it allows full flow through the pump.

   There are three pressure zones in a Vapour Core Pump i.e.

   Low pressure zone at the eye of the pump. Variable pressure zone across the impeller.

   High pressure zone in the volute.

   Typical pressure variation across the pump [5] is shown in Fig 1.

   Figure1 Pressure Vs Radius

3. Cyclic Pressure Level

   Cyclic Pressure level for LRUs of fuel systems for military aircraft, is determined by using the following expression in line with British Standard IAE 2000 [6].

   Cyclic pressure= PW FMFx FF

   Where PW = Normal working pressure FMF = Fatigue multiplying factor

   FF = Fatigue cycling temperature factor [7]

4. Approach for Cyclic Pressure Test

   One way of doing the cyclic pressure test on the pump is to divide the pump in three zones i.e. low, variable and high pressure zones and apply the respective pressure level on each zone simultaneously. In present case, geometrical design of the pump casing is such that it is not feasible to make physically distinctive three pressure zones in the pump. Hence this method can not be used for doing the test.

   Alternative to this could be an approach to apply equivalent pressure to simulate the force arising on casing due to three pressure zones. This approach is practically feasible. The same is explained below.

   1. Parameters

      Parameters which are utilized in cyclic pressure test of the Vapour Core Pump are as follows:

      Inlet (Pi) and outlet (Po) pressures are provided by designer.

      Geometrical dimensions of the impeller.

      Cross sectional area of volute.

      Type of impeller used.

      Last three parameters are available from design of the pump.

   2. Methodology for Calculating the Equivalent Pressure

      As stated above, it is not feasible to apply different pressure level in three pressure zones of the pump. Hence innovative approach has been evolved to calculate the total load on the pump casing and based on total load an Equivalent Pressure is determined. Term Equivalent Pressure is defined as the pressure level that would exert the same thrust on the impeller casing as would be experienced when the pump is running. Total force and equivalent force are calculated as follows.

      1. Force due to Low Pressure Zone

         The force exerted by low pressure zone is calculated by multiplying pump eye area and inlet pressure.

         Say, F1 = Pi x a1

         Pi, inlet pressure and a1 cross section area of eye of impeller.

      2. Force due to Variable Pressure Zone

         The force exerted by variable pressure zone of impeller is calculated by following approach.

         Total head developed by a centrifugal pump [8] is expressed by following equation.

         H= + +

         Above equation indicates that pressure variation across the impeller follows square law. Therefore, a parabolic equation in terms of pressure and radius is expressed as follows.

         P = Ar2 +B (1)

         Where P is pressure and r is radius of impeller. Following steps described the use of equation (1) for calculation of force arising on casing due to variable pressure zone.

         1. Value of constants A & B of equation (1) is calculated by substituting the following two known boundary conditions from pump specification.

            Inlet pressure at inlet radius of impeller.

            Outlet pressure at outlet radius of impeller.

         2. By substituting the value of A & B in equation (1), a general equaion in terms of P & r is achieved. This equation is used for calculating pressure at any point in variable pressure zone.

         3. Divide the impeller in concentric rings having a thickness of r starting from radius r, r+ r, r+2 r, r+3 r .r+n r. where r is the radius of eye of impeller. Division of impeller in concentric circle is shown in figure-2.

            Figure 2 Impeller cross section

         4. By application of equation achieved in point (ii), pressure level P1, P2, P3Pn at radius r, r+ r, r+2 r r+3 r .r+n r respectively are computed.

         5. Subsequent to above, the mean pressure i.e (P1+P2)/2, (P2+P3)/2 ..and (Pn-1 +Pn)/2 acting on rings of thickness {(r+ r)-r}, {(r+2 r)- (r+ r)}. .{(r+(n-1) r )-(r+n r)} respectively are determined.

         6. Having computed the mean Pressure, Force f1, f2, f3..fn exerted by each rings are calculated by multiplying average pressure and area of respective ring i.e.{(P1 +P2 )/2}X[{(r+ r)2 (r)2}], {(P2+P3 )/2}X [{(r+2 r)2 (r+ r)2}],.. [{(Pn-1+Pn)/2}X[{(r+n r)2(r+(n-1) r)2 }].

         7. Adding the force exerted by each ring gives the total variable force acting on the pump. Hence total variable force

         F2 = f1+f2+f3 .fn.

      3. Force due to High Pressure Zone

         Force exerted by high pressure zones (volute) is calculated by multiply the volute area and outlet pressure.

         Say, F3 = Po a2

         Where, Po outlet pressure and a2 cross sectional area of volute at the outlet of volute.

      4. Total Force due to all three Zones

         Sum of the three forces computed in the preceding points gives the Total force (F) acting on the pump casing i.e.

         F= F1 +F2 +F3

      5. Calculation of Equivalent Pressure

         The total force divided by total area give the equivalent pressure as below:

         P= Total Force (F)/Total Area (A)

         Where A is the area from centre of the impeller to outer diameter of volute.

         This is the pressure which is required to be developed, inside the pump during testing.

5. Methodology for applying Equivalent Pressure during Cyclic Pressure Test

   Vapour Core pump is attached with Reheat Control System during cyclic pressure test. Therefore pressure at inlet of pump is also experienced by other sub- assemblies of the Reheat Fuel Control System. Hence magnitude of inlet pressure at the pump is not disturbed.

   During cyclic pressure test Inlet Throttle Valve will remain closed and fuel in the pump is coming through a cooling hole provided in inlet Throttle Valve (ITV). Thus orifice dimension at inlet of the pump is known. Orifice dimension at outlet of the pump is required to be calculated to set the required Equivalent Pressure during testing.

   1. Orifice Design for Outlet Port

      The methodology explained below is required to find the dimension of orifice at outlet port to achieve the desired Equivalent Pressure in the pump. Path of fuel flow through Vapour Core Pump is analogous to flow through a pipe of varying cross section. The fuel flow through the pump is represented by line diagram in figure-3.

      Pump Outlet (Po & Q2)

      Equivalent Pressure (P)
      	Pump Inlet ( Pi & Q1)

      Substituting the value of FN2 from equation (5) to equation(7) and arranging the terms following equation is achieved for determining the diameter of orifice at outlet port.

      Outlet orifice

      Inlet orifice

      Figure-3 Representation of Fuel Flow

      As per Continuity Equation [9] fuel flow between inlet and outlet orifice of the pump shown in figure-3, is expressed by following equation.

      Q1: Flow at inlet orifice Q2: Flow at outlet orifice.

      Flow through an opening [10] is also described by following equation.

      Flow (Q) = Flow Number (FN) X square root of pressure drop. Hence from Fig 3.

      Where FN1 and FN2 are flow number of inlet and outlet orifice.

      In equation (3) & (4) FN1, P, Pi and P0 are known variables and FN2 is only unknown variable. From Eqn (3) & (4), value of FN2 is calculated as below:

      Flow Number at outlet is also defined as follows

      (6)

      Where k is constant and depends on geometry of hole and fluid properties. For circular orifice.

      Orifice dimension at outlet port is achieved by application of equation (8).

      Orifice of this diameter is placed at the outlet of pump to achieve the required Equivalent Pressure for cyclic pressure test.

6. Conclusion

   It is not possible to simultaneously apply the low pressure, variable pressure and high pressure in the pump for carrying the cyclic pressure test. By the methodology explained in this paper an equivalent pressure is calculated and applied to simulate force arising on the pump casing due to low pressure, variable pressure and high pressure zone. This approach has been successfully used for carrying out the cyclic pressure test on Vapour Core pump of an Aero-engine in India.

7. Acknowledgement

   The authors take this opportunity to express their sincere thanks to HAL for providing valuable inputs to write this paper. We also express our sincere thanks to Chief Executive (A), Group Director (System), GD (P) and Head of KMG of CEMILAC, Bangalore for continuous support and suggestion to publish this paper.

8. References

   1. Boyer E. Howard, Atlas of Fatigue Curves, American Society for Metals , First Edition,1986, PP-2-4.

   2. Collins A. Jack, Failure of Material in Mechanical Design, Wily Interscience Publication, Second Edition ,1993, PP-375.

   3. The Jet Engine of Rolls Royce Limited, Publication reference No.T.S.D1302, 3rd Edition, July 1969, PP 69-73

   4. Nag P.K., Engineering Thermodynamic, Tata Mc Gra-Hill Publishing Company Ltd, New Delhi,2nd Edition,1998 PP-66.

   5. Lazarkiewicz Stephen, Impeller Pumps, Pregamon Press, London, First Edition, 1965 PP- 28

   6. British Standard, International Aero Engine- 2000, Issue-2, 2000 PP-92 .

   7. Edward Shigley, Mechanical Engineering Design, Mc GraHill Book Company, New Delhi, First Edition, 1986, PP-252.

   8. Modi, P.N. & Seth S.M., Hydraulics and Fluid Mechanics, Standard Book House ,Delhi, Fourteen Edition,2002, PP-1153.

   9. Lal Jadish Dr., Fluid Mechanics and Hydraulics, Metropolitan Book Co. Private Ltd, New Delhi, 18th Edition,1984, PP-219.

   10. Green, W.L., Aircraft Hydraulic Systems, John Wiley and Sons, Chichester, Britain, First Edition 1985, PP-31.

9. Authors.

1.Shri Arun Kuma is working as a Scientist in Defence Research and Development Organization, Ministry of Defence, Government of India. He obtained his Bachelor degree in Mechanical Engineering from

Bundelkhand Institute of Engineering and Technology, Jhansi in 1998. He is member of Aeronautical Society of India. He published papers in international/ national journals. Currently his work focuses on Airworthiness Certification of Fuel System and Flight Control Actuator of military aircraft/helicopters .

1. 2.Shri Kamesh Goyal is a Scientist in Defence Research and Development Organization, Ministry of Defence, Government of Inda. He obtained his Bachelor degree in Aeronautical Engineering from Punjab Engineering College, Chandigrah in 1983. He published many papers in international/ national journals. He received best paper awards from Institute of Engineers (India), Lucknow Chapter. He is expert in airworthiness certification of Fuel System and Hydraulic System of military

aircraft/helicopters