Sen­si­tiv­ity Approach for a Tur­bop­ump Inducer Geometry

Tur­bop­umps are a crucial com­po­nent in the design of liquid pro­pel­lant space launch systems. This type of tur­bo­ma­chin­ery is used in the feed systems of the rocket engines in order to overcome the com­bus­tion chamber pressure and supply the pro­pel­lants with a suf­fi­cient flow rate to achieve high rocket thrust values.

As a result of the current demand for a reduc­tion in total weight, very high rota­tional speeds, and reduced pres­sures in pro­pel­lant storage tanks, accurate design and per­for­mance pre­dic­tion of tur­bop­umps for space appli­ca­tions is required, with the aim of max­i­miz­ing engine reli­a­bil­ity through­out its life cycle. From this point of view, it is essen­tial to include the pre­dic­tion of the possible ini­ti­a­tion of cav­i­ta­tion in the pro­pel­lant flow within the design process of the tur­bop­ump. It is also nec­es­sary to evaluate the con­se­quent per­for­mance degra­da­tion, because this type of tur­bo­ma­chin­ery fre­quently works in con­di­tions char­ac­ter­ized by fluid-dynamic and rotor-dynamic instability.

A so-called tur­bop­ump inducer has the function of raising the inlet head by an amount suf­fi­cient to prevent sig­nif­i­cant cav­i­ta­tion in the fol­low­ing pump stage. It is an axial impeller with a low number of vanes, which is arranged imme­di­ately upstream of the actual cen­trifu­gal pump impeller and rotates at the same rota­tional speed.

With the aim of eval­u­at­ing fluid-dynamic behavior, the need arises to build a system of geo­met­ric para­me­ter­i­za­tion that allows to inves­ti­gate the geo­met­ri­cal aspects that most influ­ence the per­for­mance of a tur­bop­ump inducer, min­i­miz­ing costs and times invest­ment. From the use of the software CAESES, GeoPI (Geo­met­ric Param­e­triza­tion of Inducer) was born, a fully auto­mated project workflow, in which, using appro­pri­ate ded­i­cated features, it is possible to build the complete geometry of the first com­po­nent of the tur­bop­ump, includ­ing the gen­er­a­tion of the fluid domain nec­es­sary for sub­se­quent CFD analysis. The project encom­passes a series of features that have been written in accor­dance with lit­er­a­ture guide­lines for the con­struc­tion of geome­tries such as the tur­bop­ump inducer.

GeoPI: Geo­met­ric Param­e­triza­tion of the Tur­bop­ump Inducer

GeoPI is a project ded­i­cated to the design of the inducer com­po­nent. The first com­po­nent of the tur­bop­ump has geo­met­ri­cal char­ac­ter­is­tics that allow it to operate even in very strong cav­i­ta­tion con­di­tions, to ensure that the central core of the tur­bop­ump, i.e., the impeller, can work in the absence of vapor bubbles. The design of this com­po­nent differs from the design of a classic impeller, as it has a par­tic­u­larly sharp leading edge shape and a leaning blade to ensure a small value of preva­lence to the working fluid.

As a start, in the project, the geometry of the merid­ional channel is defined by insert­ing the hub and shroud contours through B‑spline curves with four or five control points, respec­tively. The def­i­n­i­tion of the merid­ional channel also includes the leading and trailing edge, that are posi­tioned in % of the total length of the merid­ional curves. In par­tic­u­lar, the shape of the leading edge can assume a curvi­lin­ear shape as a result of two angle values defined at the hub and shroud relative to the linear ref­er­ence. To conclude this first part, it is possible to define the constant or non-constant curve that char­ac­ter­izes the blade’s tip clearance.

As men­tioned above, the inducer has a char­ac­ter­is­tic shape that dif­fer­en­ti­ates it from a classic impeller. In fact, in order to obtain its shape, it was nec­es­sary to imple­ment various routines (features) through the script­ing envi­ron­ment of CAESES. Starting from the knowl­edge of a blade angle (β) dis­tri­b­u­tion at the shroud, a wrap angle (θ) value at the leading edge, and a dis­tri­b­u­tion for the lean of the blade, this feature allows to obtain a desired number of camber curves such as to respect the value of Δθ imposed at the hub through linear inter­po­la­tion in spanwise direc­tion. For the char­ac­ter­i­za­tion of the inducer shape, the user has there­fore the pos­si­bil­ity to define the flow angle dis­tri­b­u­tion at the shroud and the dis­tri­b­u­tion of the wrap angle shift at the hub from the leading to the trailing edge of the blade, both as B‑spline curves with three/​four control points defined with respect to the M‑Prime (m’ – radius nor­mal­ized merid­ional distance) coor­di­nate. This step finally results in the camber surface, which is obtained as a lofted surface from the inter­po­la­tion of n camber curves in spanwise direc­tion, with respect to the inputs provided by the user.

The next step is ded­i­cated to the def­i­n­i­tion of the blade thick­ness. The thick­ness dis­tri­b­u­tions for suction and pressure side of the blade can be varied fully inde­pen­dently. Fur­ther­more, there is the pos­si­bil­ity to specify dif­fer­ent dis­tri­b­u­tions for the hub and the tip location, thus allowing the def­i­n­i­tion of a com­pletely free-form blade. Again, dif­fer­ent features have been imple­mented to obtain a solid blade shape with a cus­tomized def­i­n­i­tion. Each thick­ness dis­tri­b­u­tion is con­structed by indi­cat­ing the desired values for leading and trailing edge and an angle value for the shape of leading edge. The part of the dis­tri­b­u­tion ded­i­cated to the leading edge can be either linear or qua­dratic, in order to obtain the classic wedge shapes or more circular shapes, respec­tively. The thick­ness is applied normal to the camber surface defined in the first step, thus obtain­ing the final blade geometry.

Once the blade is built, it is nec­es­sary to create the geo­met­ric envi­ron­ment for sub­se­quent CFD analysis. In order to obtain a fluid domain that com­prises a single blade, a custom routine was imple­mented to obtain peri­od­ic­ity surfaces. Through this feature, for each camber curve defined above, a similar curve is obtained with upstream and down­stream exten­sions to meet the respec­tive inlet and outlet surfaces. The peri­od­ic­ity surfaces should be as aligned as possible with the blade shape and respect the θ vari­a­tion imposed between the hub and shroud sections. This concept allows to obtain an exact circular sector in the front part of the domain, avoiding any wedges between surfaces.
Inside the fluid domain, it is possible to insert upstream exten­sions to evaluate the impact of the nut intro­duc­tion and down­stream exten­sions to insert a channel shrink­age in order to obtain a more stable analysis con­ver­gence. The CFD domain is created with various BRep (Boundary Rep­re­sen­ta­tion) oper­a­tions, obtain­ing a water­tight fluid domain with closed edges.
Through the vari­a­tion of the para­me­ters defined by the user it is possible to obtain very dif­fer­ent blade shapes. Here are some examples obtained by varying merid­ional channel contours, the flow angle dis­tri­b­u­tion, the wrap angle shift dis­tri­b­u­tion, and the leading edge shape from hub to shroud section.

External Workflow with ANSYS CFX

The fluid dynamic analysis was inte­grated in the CAESES design envi­ron­ment by coupling to various ANSYS software tools. Fol­low­ing the creation of the inducer geometry in CAESES, the CFD fluid domain is exported in TETIN format, whereby dif­fer­ent colors are asso­ci­ated to each part of the geometry. This is useful for the meshing process in ICEM, which recre­ates the sub­di­vi­sion of geometry as set in CAESES and allows a repeat­able assign­ment of settings such as boundary con­di­tions or cell sizes to the dif­fer­ent patches of the geometry. Through a series of scripts, the grid for com­pu­ta­tional analysis can be gen­er­ated in a fully auto­mated way for each variant. Even the cal­cu­la­tion, directly in cav­i­tat­ing con­di­tions, is built through an auto­mated process. Each CFD analysis uses the double pre­ci­sion solver, the SST k‑ω model for tur­bu­lence closure, and the Rayleigh-Plesset model as cav­i­ta­tion model. Down­stream of the entire process, each multi-phase cal­cu­la­tion is post-processed using an in-house code written in Fortran. With this code, values of various objec­tive func­tions are eval­u­ated in accor­dance with the exten­sion and the position of the cav­i­ta­tion bubble that develops within the studied inducer. At the end of the post-pro­cess­ing step, the value of a penalty function is obtained for assess­ing the quality of the created geometry.

Results for the Tur­bop­ump Inducer Geometry

In order to obtain knowl­edge about the impact of various geo­met­ric para­me­ters indi­cated in the previous sections, an initial sen­si­tiv­ity analysis was per­formed through a Sobol algo­rithm, creating a study with 150 inducer variants.

It was decided to keep the contours of the merid­ional channel and the dis­tri­b­u­tion of the blade wrap angle shift unchanged, while three para­me­ters ded­i­cated to the dis­tri­b­u­tion of the blade flow angle at the shroud have been varied. Vari­a­tions of about one degree in the leading edge value and a complete change in the [0:1] range of the central control point of the B‑spline curve were examined. The vari­abil­ity of the x,y‑coordinates of the central control point of the β dis­tri­b­u­tion has led to sub­stan­tially dif­fer­ent geome­tries, obtain­ing very variable results in the cav­i­tat­ing condition.

The com­par­i­son with the initial geometry, through the outputs provided by the post-pro­cess­ing part, allowed to identify the best geometry among those tested. With only very small vari­a­tions in the values of the para­me­ters, an improve­ment of about 36% of the penalty function value in the devel­op­ment and spatial exten­sion of the cav­i­ta­tion bubble has been obtained. Future work will be carried out with addi­tional sen­si­tiv­ity studies on the dis­tri­b­u­tion of the blade wrap angle shift and on the shape of the leading edge, as well as through the exploita­tion of dis­tri­b­u­tions of varying thick­ness between the two blade sides.

About the Author

Many thanks to Erika Ghignoni from the Uni­ver­sity of Florence for sharing these fas­ci­nat­ing research insights.

Erika Ghignoni received her master’s degree from the Uni­ver­sity of Florence in Indus­trial Engi­neer­ing in 2017. She is cur­rently working as a PhD student at the Depart­ment of Indus­trial Engi­neer­ing in the research group ded­i­cated to the study of internal and external aero­dy­nam­ics. Her research work focuses on studying and pre­dict­ing the per­for­mance of tur­bop­umps for space appli­ca­tions. The focus is on the design of various com­po­nents and, with par­tic­u­lar atten­tion, on the assess­ment of cav­i­ta­tion impact on their per­for­mance. The study is part of a col­lab­o­ra­tion with a company of world-wide impor­tance in the aero­space field.

[1] image sources: 
rocket (https://www.ingegneriaaerospaziale.net/images/redazione/AET64.jpg)
tur­bop­ump (http://heroicrelics.org/info/h‑1/mark-3-turbopump/mark-3-jupiter-tp-cut-away.jpg)
inducer (https://grabcad.com/library/radial-type-centrifugal-pump-impeller-with-overhung-inducer‑1)